I had a flood in my finished basement in January from a sump pump failure. The salvage company cut out 16 inches of drywall and insulation (fiberglass with vapor barrier attached) from the bottom. Unfortunately, when they cut the insulation they sometimes took larger pieces of the vapor barrier. There are a few spots where I can't feel any vapor barrier (just the insulation) for as far up as I can reach my hand under the drywall. My question is basically is there anyway for me to deal with this without having to cut out more drywall? I'd like to limit the scope of this job as much as possible. The basement walls are poured concrete (7 year old house) and generally quite dry. I don't get water seeping in from the walls, for example. How bad would it be if I just put in 16 inches of new insulation (or just skipped adding new insulation altogether) and fixed the drywall (or put panelling over it) leaving the vapor barrier gaps? This past winter after the flood, I didn't notice any problems with vapor accumulation on the insulation that I could reach, although, obviously the insulation is exposed to air from the 16 inch gap. Any help is greatly appreciated.

Frankly I wouldn't worry about it. The amount of wall surface space you are talking about can't be that great. Can't do anything about it with out cutting out more drywall. Just stuff new insulation up as far as you can.
Note that it is a vapor barrier not a moisture barrier. It prevents condensation which occurs when warm and cold air mass combine. It does not prevent moisture from penetrating. Most proactive thing you could do would be to seal the wall at the floor line with caulking to prevent air movement in the wall. No air movement no condensation.

You really should have a vapor barrier, especially if you live where the climate gets cold. Water vapor goes to the point of least resistance- where there is no barrier and around doors (http://www.ezhangdoor.com/exterior-door-installation-instructions) and windows.

I would suggest a paint with vapor retarder. These paints act as vapor retarder on the outside of the drywall. This would allow you to complete the vapor barrier without removing any drywall.