A too-tight headset will make a bike handle badly. It should only be tight enough such that you don't feel any rocking of the front fork. Set properly, the handlebars should flop from side to side freely.
The front wheel being off-center could also be an issue. First, make sure it's seated in the drop outs properly. Then check to sure your brakes aren't off-center making your wheel look off-center when it's really not. If both of those things are ok, check your stem alignment (you were just messing with the headset). The only problem I can think of would be the dishing being off on the wheel but that seems unlikely. My money is on the stem.
Last edited by joejack951; 08-05-08 at 07:00 PM.