NLE's like Vegas and Premiere are awful at handling MPEG-2 input. Some of your import/project settings may be wrong (interlacing, frame size, etc). I always convert video to lossless HuffYUV or uncompressed AVI, if I need to edit it extensively.
I use Womble MPEG editing products for basic cut/splice/re-arrange.
You need to crop videos for online viewing, but not for a TV set. A good TV (including HDTVs) will hide the overscan. Even pillarboxed 4:3 on a 16:9 screen knows to chop off about 16 pixels or more from left and right sides.
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Some filters don't play nice with interlaced video. Many of them have documentation or on-screen notes mentioning this. Some don't. Feel free to list the filters you're using, if you want advice.