No major problems.
Minor interior noises.
Sluggish until the second cam profile.
Cloth seats are very delicate.
Air conditioning vents are difficult to manipulate to the desired, comfortable position.
Even though it's not as fast as a GT-S, the GT is quick and nimble.
The Celica has very great handling.
No large after-market support yet.
Great looking car. I get so many positive comments at car shows and from the ladies.
The orange dash display can get annoying.
The double din setup for the CD player/radio is not my favorite type.
One thing I've noticed from the early 90's is that the Celica's rarely have aftermarket support. While you do find one here and there (rodmillen.com, nopi.com, etc) aftermarket kits & parts are brutally expensive as compared to the Civics & Integras.
A couple pros of this though are: it keeps up the "goodwill" of the car, you're not surrounded by testorone-excessed teenagers looking to race, the car turns heads with the factory body styling.
A couple cons of this are: Toyota has to develop expensive bodykits themselves because they know the aftermarket people won't do it right away (and so you pay Toyota $$ for it), when you find aftermarket parts etc they are costly. Lastly, it's hard to convince people to give the car a try or to buy one because it's expensive to own if you plan on making modifications.
Take care and good luck!