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.