We do the following:
a) Check the OM alt vs. the approach plate alt (+/- altitude correction which depends on the given temperature on that day, this having been done during the briefing)
b) Check/confirm the MDA (CAT I) or DH (CAT II/III)
c) Check that the correct Missed Approach Altitude is set in the Altitude window of the altitude alerting device at hand.
d) be configured properly for the landing (pitch/power/speed/config etc...)
Oh yes, the altitude difference (temperature above/below ISA) one might have at say the FAP/OM becomes less and less as one approaches the MDA. How much less depends on the actual difference and is not that easy to quantify me thinks. DH is a different matter as one is using Rad Alt. If one has RA then use it during the approach to compare the DME with it. Obviously the DME is not always at the threshold but it gives one an idea of whether the baro altimeter is functioning properly or not. (+/- 300 ft per DME)