One to be careful of is not having it on Amps when measuring Volts ... or having it on a too low range when measuring Amps (although some are fuse protected).
So, if say you are looking for a very low current drain but there is an initial inrush current as you first make the circuit with the meter (in series) ... keep the meter clips shorted together as you first hook up (low voltage stuff only etc).
This wouldn't apply to you MM but a mate texted me a while ago asking if a 20mA drain would flatten a battery over a few days. I said it probably would but suggested he leave the meter in place for say half an hour and check again. He texted back to say it dropped back to next-to-nothing after 20 mins or so. ;-)
Cheers, T i m