That's impressive. I've heard and the product manuals of most multi meters talk about the risk of shock when opening it up. Does anyone know how likely or rare that is?
You can discharge a capacitor by shorting it with a screwdriver (with an insulated handle), or by clipping a resistor to the capacitor leads for a less abrupt discharge. I think people who do a lot of appliance repairs learn to look carefully for capacitors when opening appliances, and make sure that any moderately large ones (or ones that there was reason to believe could have been charged to a high voltage) are discharged before beginning work.
I don't know how common large capacitors are in multimeters. I think there's a much bigger risk when opening a CRT monitor or a microwave.
Most multimeters are battery powered - this one is the exception, this one is a bench meter and is supplied by an IEC cable on the rear, but so long as you unplug in and let it sit for 30 seconds or so before opening it up, you're just fine.
You generally only have to worry about capacitors being charged still on tube-type gear (anything with high voltage circuits), anything with solid state parts, will self discharge within moments.
Obviously, do not have the meter hooked up to a circuit under test while working on it.