Im on my iPhone 4 and whenever I try to watch ANY video, something pops up saying "You do not have permission to access the requested resource". I tried turning off my wifi but it didn't help. Any ideas?

Check your network carrier data is on and also check the YouTube settings is anything is blocking to access YouTube.
You can also reset network settings once and try again.

Your internet connection source might have blocked YouTube. Check the internet source again.

Close all the apps and restart.
Double click the home button. Now the opened programs will be displayed. Hold your finger on one of the application until it starts shaking. Now click on the x floating on the icon.

There might also be a restriction setting in general settings.

hope this helps.
Grant