Try: Select a vertex on your 'fake' mesh and use 'select more' until you it either selects the whole problem mesh and not the original, or it selects everything. If it's just the bad part, try deleting it. If everything is selected, you may have hit 'extrude' with the whole mesh selected. There is a feature that may be called 'ghost' or 'onion skin' but the idea is that it shows you parts of an animation ahead o behind your current time. If you have an animation on your mesh, check to see that this feature is not enabled.

A less likely cause may be you graphic display driver or hardware. Try adding a new object and see if it has the same issue. if it does, check your older files to see if they have this problem too. Then try opening on another computer. If its fine on another computer, try resetting your graphic card driver settings to defaults (advanced graphic cards have lots of settings to tweak in their drivers) and if that doesn't work, try reinstalling driver. Last resorts are to reinstall maya and If your computer has built in graphic chipset, try taking out your graphic card and running of of that. If it's fine at that point, you may need to get a new graphic card.