...but 5 does not mirror as 2! It inverts though. The only numbers that mirror correctly are 0, 1 and 8. In the constraints of the original question I think that the only times that are the same as the real time when viewed in a mirror are

0000
0110
1001 and
1111

The only times an analogue clock with no numbers on is correct in a mirror are 12, 12:30, 6, 6:30, 3:15, and 9:45

If you ignore the length of the fingers you could have other combinations so an analogue clock gives more scope :-)