I am able to do so in 10.8.2:
Have you tried deleting
"com.apple.TextEdit.plist" in
Macintosh HD / Users / YOU / Library / Preferences / yet?
Does it also happen in another, even temporarily created, user account?
I've been doing this for ages, dragging images, copy and pasting selections into TextEdit, no problem until recently. I'll try this and see. Using another account is a good idea. I'll report back.
Updated: OK, this is strange. Did they make a fundamental change to OSX organization with the versions of OSX newer than Snow Leopard? Where I used to have a Library folder in my Home folder, I have none. There is a Library folder in a Shared Folder, but all it has within it is Application Support. Could these folders now be invisible? More checking needed. More help appreciated.
Thanks!
Update 2: OK so it is invisible. Found it...
here.
Update 3: Trashing the TextEdit plist does not solve the problem...