You mentioned something though, that I have encountered many times in Final Cut. Make sure your footage was not brought in as interlaced footage - that would cause the effect you're talking about and for some stupid reason, Final Cut will bring in progressive footage as interlaced some times. Right click on your image in your timeline and select "Item Properties", then "Format"....make sure the Field Dominance is "NONE". If it's not, right click on whatever it is and select "NONE".
The only other reason I could think of as to why your image may look like you said is you output it to an interlaced image...?