The following AppleScript adds a word (and character) count pop-up dialog to TextEdit:
tell application "TextEdit"
set word_count to count words of document 1
set char_count to count characters of document 1
set show_words to (word_count as string) & " words. (" & (char_count as string) & " characters.)"
set dialog_title to "TextEdit Word Count"
display dialog show_words with icon 1 with title dialog_title buttons {"Ok"} default button "Ok"
end tellOpen AppleScript Editor's Preferences, and on the General tab, turn the 'Show Script menu in menu bar' option on. You'll then have a script icon up there, near your clock.
Now, with any TextEdit document in front of you, you can access your Word Count script from the Script menu in the menu bar. When you do, you should get a small dialog saying something like:
TextEdit Word Count 2832 words. (15060 characters.)The 'OK' button dismisses the dialog box.
[crarko adds: I tested this, and it works as described.]

