The templates are served via json and it is possible to make a template that breaks the json and causes script errors.
What I would do is copy your custom templates into a text editor to keep a copy of them but remove them one by one and see if removing one of them fixes the template dialog. If you isolate the one that is causing a problem, I would look for things like apostrophes. If it has single quotes try double quotes or if it has double quotes try single quotes. I can't remember what combination causes it but I've seen issues like that break the template dialog.
I don't think it is a really an upgrade issue, probably just coincidence that you noticed it soon after upgrading. Or are you saying you got this error with a new clean installation?
Hope it helps,
Joe