How do I fix the shelf support holes in my cabinets?
The metric (4 or 5mm) holes can be redrilled to hold the 1/4" shelf spoons. If that does not do it, there are metal sockets for the 1/4" spoons that take a slightly larger hole, then they can be driven into place to hold the larger spoon. 
If the spoons or clips already have a 1/4" hole, then you may be better off retro fitting a shelf track system. Third pic.

Instead of trying to drive nails in a tight space, use 4ga X3/4" screws instead, the cabinet will thank you for it.

        

The picture size is grossly out of proportion, buit the first pic is the socket that holds the spoon which is the second pic. The socket looks more like a bucket, that will hold 10 of those spoons..