It sounds like your pot is hooked up wrong or something electrical is wrong with the Mega since you said the Uno works.
Did you try running the A0 pin straight to ground? Just to see if the Mega will report back 0? If that works take the wire out of A0 completely and see what the results are. 'Normally' you get fluctuating values. If it comes back as 1023 there is a problem.