https://en.m.wikipedia.org/wiki/Telicity

I don't think those additions are very useful.

As for me, I don't mind having those notes. But the question of usefulness for the average user remains.
That said, I believe there's no easier way/term to explain this with, the english wikipedia article on telicity is certainly enough to understand the implications of this note.
What do others think?

登っている (atelic) -> to be climbing
上がっている (telic) -> to have raised

Probably worth adding to the note?

@@ -30 +30 @@
-<s_inf>after the -te form of a verb; indicates continuing action</s_inf>
+<s_inf>after the -te form of an atelic verb; indicates continuing action</s_inf>
@@ -37 +37 @@
-<s_inf>after the -te form of a verb; indicates continuing state</s_inf>
+<s_inf>after the -te form of a telic verb; indicates continuing state</s_inf>

I agree that having "to have ...-ed" first is far more typical for this sense. 
That "construction phrasing" is to my knowledge the standard used in grammar books, and is also taught this way in school.
On its own "to be ...-ed" were more likely to be associated with the passive, that is true, but I think that together with the note the implication remains clear. As nonさん mentioned, "(to) be" also used to be a perfect helper.
Hence one could translate 座っている as "to be seated", which does sound rather formal, but I have nonetheless certainly heard before.

I also agree that it is outright impossible to account for the immense amount if irregularities present in English verb inflection. Hence keeping the sense short but succinct being a good option.

Lastly I believe that having this sense is an improvement one way or another. As someone who has little time to devote to actually studying Japanese, the fact that the aspect indicated by (て)いる varies depending on the telicity of the given verb has long eluded me. So having this in JMdict is overdue in any case.
I believe that a Japanese learner with a sufficient knowledge of the English language will understand what sense four represents.

Apologies for cluttering the feed, but I must correct myself: in line 20 (3rd line from the bottom up) I said 'past participle', I meant to say 'passive voice'.
Just so this is not complete clutter, I adopted the suggestion of shifting the order of 'have -ed' and 'be -ed'.

@@ -37,0 +38 @@
+<gloss>to have ...-ed</gloss>
@@ -39 +39,0 @@
-<gloss>to have ...-ed</gloss>

I would not get too caught up in cases like すわる versus 'to sit'.
Were language an exact science, we would have "I have sat" as a direct equivalent which, as pointed out, is not the only option and 'I am sitting' is just as acceptable and arguably more so.
However, this ambiguity is due to the verb 'to sit', and is not an English generalisation: once again, you cannot take 死んでいる to be 'dying' or 至っている to be 'arriving'.

The matter is that the Japanese すわる acts like a telic verb by default, while 'to sit' does not.
'To sit' patterns like an atelic, dynamic verb like 'to run' in most cases, e.g. you can say "I am running" and "I am sitting" as well as "I sat for an hour" or "I ran for an hour" but not "I sat/ran in an hour" while a verb like 'to die' (which like the Japanese 死ぬ, is telic) assumes a rather different meaning when made into "I am dying" or "I died for an hour", and can be used with an in-adverbial very easily.

With a verb like 'to die' -ing shifts the meaning of the verb from "undergoing death" to "approaching death", while the for-adverbial refers to the duration of the post-state following the verb (in cases where it even applies), rather than the duration of the event itself like with 'sat' or 'ran'.

But then again, "most cases".
"I ran in an hour" for example, can be used so long as either the rest of the phrase or the context provides a delimited something to be run, such as a kilometre, which would then change the verb from being atelic to telic.
'To sit' too has its peculiarities in that "I am sat" means the same as "I am sitting" in most contexts - and note here that 'am' is also an old perfect auxiliary (famously, there is the phrase "I am become death...") though it could be argued that most people do not think of it as such, and that it has its own particular nuance when compared to 'have', e.g. "I am gone" versus "I have gone". 
And then, even 死んでいる which unarguably should be a perfect by default, can be reinterpreted as a continuous, iterated event in phrases like 「そして、おびただしい数の生命が、毎日、死んでいる」。
...Also, could it not be held that the previous "Sat for an hour" instead of the referring to the duration of an event, is instead referring to the duration of the post-state to act of sitting, just like "Died for an hour" refers to the post state to the act of dying? Maybe "I am sitting" is the odd one here...

All this is to reiterate what I opened with: there is too much aspectual doohickey to turn "mismatches" like 座っている　and 'sitting' into a central issue, aspect is not inflexible and a verb can often belong to several categories, or have their categories completely altered by adverbials and context.

About 'be -ed' as a gloss: I included it because of cases wherein, putting the debate on nuances aside, the auxiliary tends to and/or can be 'to be' instead of 'to have', for example "He has gone to tend to family matters" and "He is gone to tend to family matters", etc.
That it is the same configuration used for the past participle, is an unfortunate coincidence (or perhaps it is not, but I digress).

Lastly, regarding "have/be -ed" excluding other past participles: well, that is the nature of irregular verbs. For multiple reasons, we cannot list every single past participle, and what that leaves us with is to indicate the regular form. But I do not think that to be a problem as 'have -ed' really stands for a formula of 'have + past-participle', and applying it to a verb like 'to fall' has the output of 'have fallen'.

座っている, being formed from a 瞬間動詞, falls under the 4th sense of 〜ている, which indicates a resulting state from a completed action. However, depending on context could be translated as "to be sitting" (state, not continuing action) and not "to have sat." English translations are pretty ambiguous when it comes between these two senses.

Additionally, in the 4th sense "to be ...-ed" can easily be mistaken for passive voice, which is misleading. I think it should either come second or be removed. It also assumes regular "-ed" verb forms in English, ignoring many natural equivalents like "to have sat", which but doesn't follow the "-ed" pattern.

In truth, dictionaries - including the Daijirin I used - often even distinguish between subtypes of perfects, but I do not think much is gained from the distinction as they are variations upon the same theme.
Viewing the relation between habituals and progressives the same way, I would not get into habituality as just leaving it with the "be . . .-ing" gloss is probably enough, since a reader faced with 「毎日パンを食べている」would render "I am eating bread every day" and that would be readily understood as habitual. 

In contrast, trying to translate 「死んでいる」 as "dying" is quite distinct from the "died/dead" that it actually means.
And lastly, it is worthy noting that an habitual reading must be forced by either an adverbial or context. Without either「パンを食べている」defaults to being a single-instance progressive, unlike「死んでいる」 which forces a perfect reading because of the meaning of the verb itself.

This is further substantiated by other references as well, like shinsen, smk or meikyo.

Smk even has three senses, having included a sense for habituality as well:
㊀動作・作用が、継続・進行して、その時点に至ることを表わす。
「今手紙を書いて━ところだ」
「泣いて━のか笑って━のか分からない」
㊁動作・作用が反復的に行なわれることを表わす。(Meikyo has this as well)
「毎朝パンを食べて━」
「欠かさず日記を付けて━」
㊂動作・作用が完了したままの状態であることを表わす。
「ドアが開いて━」
「あの人とはどこかで会って━」
「仕事でとても疲れて━」

.

I would be in favor of having separate senses for progressive and perfect usage. It's more tidy and possibly clearer to users while also in accordance with references.

As for the habituality sense in some refs, I'm not sure if or how it should be included. Maybe someone else has an opinion on this?
AFAIK it isn't obligatory to use ている when talking about habits or routines, but I could be wrong

[v1,aux-v] ⇒ [aux-v,v1]

@@ -26,0 +27 @@
+<pos>&aux-v;</pos>
@@ -27,0 +29,5 @@
+<misc>&uk;</misc>
+<s_inf>after the -te form of a verb; indicates continuing action</s_inf>
+<gloss>to be ...-ing</gloss>
+</sense>
+<sense>
@@ -28,0 +35 @@
+<pos>&v1;</pos>
@@ -30,2 +37 @@
-<s_inf>after the -te form of a verb; indicates continuing action or state</s_inf>
-<gloss>to be ...-ing</gloss>
+<s_inf>after the -te form of a verb; indicates continuing state</s_inf>

Daijirin: 「㋐主体の動きを表す動詞に付いて、その動きが継続・進行中であることを表す。」is distinct from「㋑主体の変化を表す動詞に付いて、その結果が持続していることを表す。」

"Be -ing" does not fit as a translation for verbs with a defined terminal endpoint and ensuing post-state such as 死ぬ, 消える, 終わる, etc. wherein the -ている auxiliary does not indicate a progressive and thus cannot be translated as -ing.
E.g. 死んでいる means either "is dead" or "has died", and not "is dying"; 終わっている means "is finished" or "has ended" and not "is ending", etc.
This is a peculiarity of the ている auxiliary in that it doubles down as both the progressive and perfect marker, varying according to the verb, whereas English has a different strategy for each independently of the verb.

I have also removed "have been -ing" as that is perfect progressive, which does not correspond to ている that is either perfect or progressive, but not both.
(That, and the English perfect progressive is not always in practice just what you would in theory get from a simple sum of the perfect plus the progressive, but I digress)

Alternatively, a separate sense could be made for the perfect:
[3][v1,aux-v][uk]
  [note="after the -te form of a verb; indicates continuing action"]
  to be ...-ing
[4][v1,aux-v][uk]
  [note="after the -te form of a verb; indicates continuing state"]
  to be ...-ed; to have ...-ed

@@ -32 +32,2 @@
-<gloss>to have been ...-ing</gloss>
+<gloss>to be ...-ed</gloss>
+<gloss>to have ...-ed</gloss>

I'd leave the [rk].

@@ -7 +6,0 @@
-<ke_pri>ichi1</ke_pri>

BCCWJ:
 いる-非自立  iru	968,064   
 いる         iru	95,901   
 居る         iru	5,247   

5,247/95,901 = 0.055 = 5.5%


Massif for が居る
https://massif.la/ja/search?q=が居る
Out of the first 100 results 3 sentences use 居

I'd still argue that it is rather rare. 
I can see, however, how it could come into conflict with our policy. 
What to do here? Just revert to how it was before?

が居る  1,290,725   7.2% 
がいる 16,517,702  92.8% 

ている 715,720,121  99.9% 
て居る     450,959   0.1%

not that rare for senses 1 and 2.

Google N-gram Corpus Counts
╭─ーー─┬─────────────┬───────╮
│ 居る │   5.321.828 │  0.7% │[rK]
│ いる │ 804.530.319 │ 99.3% │
╰─ーー─┴─────────────┴───────╯

[ichi1] tag would need to be removed

@@ -5,0 +6 @@
+<ke_inf>&rK;</ke_inf>

@@ -15 +15 @@
-<xref type="see" seq="1296400">在る・1</xref>
+<xref type="see" seq="1296400">ある・1</xref>

Reverting.

@@ -17 +17 @@
-<gloss>to be</gloss>
+<gloss>to be (of animate objects)</gloss>

An edit like this needs to include detailed reasons.

@@ -17 +17 @@
-<gloss>to be (of animate objects)</gloss>
+<gloss>to be</gloss>

@@ -32 +32 @@
-<gloss>to have been ...-ing)</gloss>
+<gloss>to have been ...-ing</gloss>

So would I.

@@ -30 +30 @@
-<s_inf>after the -te form of a verb; indicates continuing action or state; the い is sometimes dropped</s_inf>
+<s_inf>after the -te form of a verb; indicates continuing action or state</s_inf>

I'd be happy to remove "the い is sometimes dropped" from the note.

@@ -30,2 +30,3 @@
-<s_inf>after the -te form of a verb, the い is sometimes dropped</s_inf>
-<gloss>verb indicating continuing action or state (i.e. to be ..ing, to have been ..ing)</gloss>
+<s_inf>after the -te form of a verb; indicates continuing action or state; the い is sometimes dropped</s_inf>
+<gloss>to be ...-ing</gloss>
+<gloss>to have been ...-ing)</gloss>

Move note about appearance "after the -te form of a verb" from 
gloss to actually a note.

@@ -30,2 +30,2 @@
-<s_inf>the い is sometimes dropped</s_inf>
-<gloss>(after the -te form of a verb) verb indicating continuing action or state (i.e. to be ..ing, to have been ..ing)</gloss>
+<s_inf>after the -te form of a verb, the い is sometimes dropped</s_inf>
+<gloss>verb indicating continuing action or state (i.e. to be ..ing, to have been ..ing)</gloss>

@@ -22,0 +23 @@
+<misc>&uk;</misc>
@@ -27,0 +29 @@
+<misc>&uk;</misc>

@@ -15,1 +15,1 @@
-<xref type="see" seq="1296400">在る</xref>
+<xref type="see" seq="1296400">在る・1</xref>