It is most likely a field order issue which can be introduced in several ways. it you crop or move video an odd line you can introduce this issue.
The problem is also unsolvable unless you have an external monitor for your FCP system. WIthout this key piece of equipment you have no idea when and where the problem is being introduced. I just fixed a documentary with the same problem, no idea how the guy got it so messed up but without me playing the timeline out to a TV there would be no easy way to fix this.
Couple things to check, first does the original DVDs play okay with regards to this camera angle? If yes, make a m2v and DVD from your converted file, if it plays okay you know you introduced the problem in the editing process. If the converted file plays back okay tell us what you did to they angle, is it one of the 4:3, did you scale it? reposition it?