Read through this. It seems like a lot, but it is the single best read for our cars.
http://www.grandprixforums.net/threa...ding-Your-3800!

Weak points would be:
Lower intake manifold gasket (came plastic from the factory, WILL leak coolant into the oil. Replace with the metal revision)
Transmission (while not weak per say, once you start dumping power to it, you need to consider upgrading some hard parts)
Rust. Depending where you are, check all common rust areas (especially the strut towers)

Best thing to wake the GTP up is a tune. An intake/headers, tune and a pulley drop will get you quite a bit better performance out of them. After that, consider camming (or higher ratio rockers), intercooling, spraying meth, alky, water, etc.