Here are a couple of examples to support my contention that つま先 deserves to have "toes" 
(of a human or animal) mentioned explicitly in the definition, and in the plural form, 
and not just suggested as a less-likely possibility, as in the present definition:
"toe (esp. of shoe, sock, etc.)"
.
1) The tops of these shoes press my toes.
この靴は先がつま先に当たる。
2) As the obstruction worsens, a person may develop sores, typically on the toes or heel 
and occasionally on the lower leg, especially after an injury.
閉塞が悪化するにつれて、典型的な場合にはつま先や踵、時には下腿にびらんが生じることがあり、これは特に外傷後に起こり
やすい。
Source: jukuu.com

It doesn't mean "tiptoe" in the usual noun sense:
"a standing position in which the heels are raised off the ground and the weight is on the front part of 
the feet, with the body often also stretched up to gain extra height" 
(Encarta)
"the position of being balanced on the balls of the feet and toes with the heels raised —usually used 
with on"
(Webster)
.
Webster says it can mean "the ends of the toes", but I think that's not a common usage of the word 
"tiptoe". You don't say "I injured my tiptoe". The unambiguous "tips of the toes" can be used instead.
.
From the Wikipedia article, it seems to me that the main meaning is "toes" rather than "tips of the 
toes":
爪先（つまさき）とは、動物（特に人）の足の先端部の指がある部分、または足の指の先の部分のことである。英語のtoeからトーとも言う。一本一
本の指に着目する場合には足指（あしゆび）という場合もある。
http://ja.wikipedia.org/wiki/爪先
My translation: Tsumasaki, in animals (and especially humans), refers to the front part of the foot 
where the toes are, or to the tips of the toes. It is also called "tou", from the English word "toe". 
When focusing on the toes individually, they are called ashi-yubi.
.
That's why I give the plural definition "toes" rather than the existing definition "toe" -- つま先 seems 
to refer to the toes as a whole, and not to individual toes.
.
Note that the Wp article says that digitigrade animals walk on their 爪先:
"多くの動物は、爪先のみを地面に接して立っており、これを趾行動物（しこうどうぶつ、digitigrade）という。"
爪先 here translates as "toes", not "tiptoe" or even "tips of the toes":
"A digitigrade is an animal that stands or walks on its digits, or toes." 
http://en.wikipedia.org/wiki/Digitigrade

@@ -19,2 +19,3 @@
-<gloss>tiptoe</gloss>
-<gloss>toe (esp. of shoe, sock, etc.)</gloss>
+<gloss>toes</gloss>
+<gloss>tips of the toes</gloss>
+<gloss>toe of a shoe, sock, etc.</gloss>

GG5, etc.

@@ -20,1 +20,1 @@
-<gloss>toe</gloss>
+<gloss>toe (esp. of shoe, sock, etc.)</gloss>

Adding the more general meaning of "toe".  It's defined that way by several sources at http://ejje.weblio.jp/content/爪先

@@ -20,0 +20,1 @@
+<gloss>toe</gloss>