You should not attempt a serious edit by only looking at the computer monitor for judging quality.
FCP is designed to be operated with an external video monitor connected
(through a camcorder is just fine) DURING the edit process.
The external video monitor should have shown you any flickers or “image buzzing” before output.
Try this:
Apply the Video Filters > Blur > Gaussian Blur.
Adjust the setting to 0.25 and keep adding “more” (up to 0.75 or even 2.0) as you observe the results.
As images (moving or stills) are more “complex” they can “buzz”on the video screen.
Adding the Gaussian Blur Filter can create an image that looks smoother.
You need to RENDER the effect to view full quality on the external monitor.
In FCP 5 set your video processing to “Best Quality” (It defaults to “Normal”).