Ok, I'm stumped. No matter what I try, I cannot log into my YouTube account using the iPad app. I cannot login using the app on my iPhone either. I've tried the application specific password and that didn't work. Anyone have any ideas?
Try a reset. Press & hold the Power and Home buttons together for 10+ seconds, ignoring the red power-off slider, until you see the Apple logo. If that does nothing to solve the issue, then it is likely times to restore the iPad to its factory settings.
Already thought of that and it didn't work. I did manage to get Safari to properly display YouTube by deleting cookies and clearing history and cache. Was able to login using Safari, but not using the app.
Problem resolved. Created a channel and a username (In addition to the email address the YouTube account is connected.) Now I am able to login in the YouTube app using the email address or the associated username.