Well, my initial thought would be that it is a resolution or topology type issue, but as you said you have checked both of these, my next thought would be it sounds like either a projection/translation issue and/or a corrupted MXD issue. I would suggest starting with checking that the projection of the data being edited matches the projection of the dataframe it is in within the MXD (Dataframe > Properties > Coordinate System tab). If the projections match, then I would try making a copy of the MXD and running MXD Doctor application on it and see if it is a corrupted MXD issue that MXD Doctor can resolve (Should be in Start Menu> All Programs > ArcGIS > Desktop Tools > MXD Doctor, or at least that's where it is on my system). If nothing so far has helped though, as always with ArcGIS Desktop, try creating a new MXD and add the same data in (checking and making sure you set the dataframe to the correct projection to match the data's) and see if you experience the same issue. If a new MXD solves it, then you should be able to go back to the original MXD and bring in the layers by copying them in and/or saving the layers (or layer groups) out as layer files and bring those layer files into the new MXD.
Unfortunately, if you are still experiencing this issue after all of that, I would have to suggest calling ESRI Tech Support as it would seem that would almost have to be a software bug they should be aware of.