I'm looking for software that can perform simple edits without transcoding the video. I don't want the software to recompress the video, making it more lossy than the original source was. I know there are similar tools that avoid transcoding audio. I figure there might be something for video, as well.

I only need it to trim black bars and sloppy edges from videos. I don't really care about other features.

Not going to happen. You can't just change the frame and expect that the encoded frame isn't going to change. In some cases you might be able to just drop macroblocks, but I don't know nearly enough about video encodings to say for sure what would make that possible or even if there are tools to do it (inclined to think no).

About the closest you're going to get is do the trimming, then do a two-pass encode to match the previous file size, in which case the quality loss should be marginal.

Yeah, that sounds about right to me. You can't even simply drop frames out, because most encoding schemes do frame addition or merging of some sort starting from occasional keyframes, so dropping a frame will make subsequent frames be missing data until the next keyframe.