I’m playing it now, I haven’t noticed any serious glitches. Also, the game asked me to sign-in to the Playstation Network when I first started it up, I said “nope” and it hasn’t bothered me since.
Edit: Ok, scratch the part about not running into glitches. Just within the past five minutes the right trigger has stopped registering twice and I’ve had to restart the game to get it to come back.
For anyone interested, Chrono Trigger is part of the Steam Spring sale for just $3.74. It’s absolutely worth that price.