There are many causes for glass to get hazy in the kiln. This effect can be prevented by using specific cleaning methods, and possibly by venting your kiln (if you are using some form of refractory paper as a shelf release). To help you prevent the haze, we would need more details about your cleaning and firing methods.
As far as the tops sliding, I haven't seen this happen in the kiln. Do you use any kind of glue to stick the cap to the base? If so, might the glue have water evaporating, or otherwise off-gassing to the extent that the glass moves before it has heated up to softening temperature?
As far as fixing the haze: you can sandblast the piece and refire (as Charlie suggested in another thread recently) or you can sprinkle clear glass powder on the properly cleaned piece and refire. But you might want to delay refiring until you understand what caused the haze in the first place.
I hope this helps.