Kaji01 wrote:opened it up in Streamclip, and then simply saved as MPEG
I think that is your basic problem right there. You haven't said which MPEG codec you are using, but all of them are pretty poor choices for editing because they have so many reference frames (P - predicted, and B - bidirectionally predicted) in them. You really want to be using something where every frame is an I (intra) frame, i.e. every frame has the whole image in it.
If you place a cut on a B or P frame then the editor has to dive into the GOP (group of pictures) and produce an I frame for the start of the new clip. Sometimes this happens after the fact - like during a render or an export, but in general you aren't supposed to notice that this even going on.
Clearly you are noticing the process (and I am not sure why), but I suspect that it would probably look fine in an export.
Obviously being forced to export every five minutes to check on your edits is a non-starter, so I go back to my original statement: Don't edit in one of the MPEG's* use something like DV, or lossless if you can do that.
* That said, editing MPEG2 source in MPEG2 when it is destined for MPEG2 is often just fine, unless you have lots of effects.