Glitchy Video Playback and Renders

I'm having issues with videos downloaded from this site.

The program monitor is often glitchy during playback (see image below) and these glitches carry over into the render. In an older version of Premiere I was previously using, this glitch only showed during playback and not in the render so it wasnt a big deal, but with it affecting the render now they're not usable at all (unless I run them through all through a converter which would be very tidious).

I'm wondering if the FPS could be the issue? Videos downloaded from this site seem to have an obscure and variable FPS (ex. this video in the screen shot is 58.96 FPS). and I've seen others with the same FPS +/- .50-ish. I mention this because my sequence is a flat 60 FPS.