I just bought my car,1998 contour GL (zetec)Auto.
Is there anything that I need to do to it?(for performance)
And, what are the common problems with it?

To add longer life - add an additional transmission oil cooler. VERY IMPORTANT MOD & will save you some headaches in any car you own with an automatic. Cost: about $50 for parts, do it yourself.

Performance - After you do your other performance mods (i.e. intake/exhaust), find a nice source for a Superchip. It'll change your shift points, give you smoother shifts, & give you better overall performance. Cost: about $200