Check engine light comes on repeatedly.
Plastics or splash shields are likely and have fallen off.
The car stutters and hesitates frequently at start up, or after driving for extended periods of time.
Lift back shocks stopped working very shortly after I purchased the car, and cost $300 a pair from the dealer to replace. (More expensive than the shocks and struts of the vehicle suspension).
Engine has had a loud knock and tick since 2005.
The car is extremely noisy inside the cabin.
Would trade my Celica for my old Prelude in a heartbeat, despite spending over $25,000 on financing this junk.
Seats are uncomfortable.
The visibility of blind spots is horrible.
Another good reason to buy a domestic car. Your Celica sounds almost as bad as our Honda Civic. We drive Ford and GM now. No problems at all.
I own a GT myself, and the little things happening are just typical for a Japanese car as the miles get up there. My shocks are shot, I've got to watch my oil a bit more, but if you take care of it, it will take care of you.
You mention a strange "tick"...the VVT-i system produces valve tick, which is not uncommon on many 4 cylinder motors. From what I've researched on Celica forums, it's nothing really to worry about; it comes and goes. I'd say just keep putting miles on your Celica and try to take care of it.