A while back I was looking for a mpeg2 editor and I got so many different opinions, so I had to figure it out my self, so I want the same input from you but in terms of mpeg1 please give the name and your experiences and bad and pros as well.
The best Mpeg 1 editor(Cutter and Joiner) IMHO is Womble MpegVCR. Unlike many editors it makes GOP perfect edits(Google that problem). Also try Video Redo if you have problems with your Mpeg1 File. This is the best software for fixing Mpeg1 File problems(not for editing).
For free versions I would try CutterMaran OR Mpeg2Schnitt but many people have reported Sync problems with the output by these methods.
Also General purpose softwares which also include Mpeg Editors(Cutters and Joiners) is TMpGenc(there is a freeware version which can be used only for editing Mpeg1 from Pegasys Inc-Google that).
Hope this helps.
I found VideoReDo to be the best editor. Less overhead, no image distortion as others, and exact frame capability.