AviDemux has Smart Copy if you are cutting a file in Copy mode and do not select an I frame as the end point. It will ask if you want to use Smart Copy to "fix" the broken frames. This only works on certain, supported codecs like divx or xvid as far as I know. Any time AviDemux asks if you want to use Smart Copy, say yes.
AviDemux is not very good with mpeg files though. It has been known to cause video/audio sync problems when cutting. Better to use VideoRedo or one of the Womble programs for that.