iPod touch 4th Generation iPod touch having issues signing in to certain things

My girlfriend is having issues signing in to FaceTime, Twitter, AIM, etc. on her iPod touch.

FaceTime says "An error occurred during activation. Try again."

Twitter says "Could not authenticate you. (The certificate of this server is invalid. You might be connecting to a server that is pretending to be "api.twitter.com" which could put your confidential information at risk.)"

Any idea what the problem is? She has no problems with any of these services in Safari.

Also, restoring isn't really an option because she is nowhere near a computer.

Anybody?