Video Lag and quality fix?

Hey fcp world!

So I've started out an editing project. The footage that was given to me to edit was really bad. Some I fixed using grain etc but there's some videos that have these vertical lines while on movement. The camera that was used is an amateur Sony Handycam (hard drive) and the original format was .MTS, I converted everything into .mov to work it in Final Cut X and Motion 5. Is there a way to fix the quality of these videos and remove or lessen those vertical lines? In Premiere Pro there's a built in option for fixes like this but I don't use it that well.

Thanx for any help!

Can you post a sample clip?

I just did, it doesn't show pfff... I've posted it on YouTube though and you can see the lines. Just put it in fullscreen.
(it's in the original quality)

Ah, interlace video artifacts. They show up when things move a lot or quickly. Two options. Either edit it in an interlaced timeline, or convert them to progressive video (which is what I would do) before editing, and edit in a progressive timeline. This is simply an issue with standard definition video.

well... how do you do that? Sorry but I'm kind of a starter!

Never mind I think I got it! thank you!!!

Did it, didn't work. Still Interlaced. Also the clip seems to already be in progressive. I even exported it with compressor and added and deinterlace filter but nothing. Does it matter that it is at 30fps?

If it is progressive already, then the interlaced artifacts may have gotten baked in and can't fix it, as far as I'm aware. But that is interlacing artifacts. You'd need the interlaced original.

Thank you very much! I'll try compressing it again from it's original, wich is .Mts but I think it's already burnt in.