Just a guess, but your sequence is probably set for DV Compression, which is pretty severe. Unfortunately, if you are printing it out to tape, it won't look that good. However, if you're just making a QT video, use a different codec.
To do that in final cut pro, you would select sequence>settings... and then you would choose a preset. DVCPRO50 will look a lot better. Uncompressed or animation codec will look the best but also give you the largest file size.