The first things i normally check off the top of my head (assuming there's no outstanding finance on it, it's not a cat N etc):
General condition inside and out - does it look like it's been looked after. Scratches, scuffs, anything grubby inside, high wear on a drivers seat bolster on a lowish mileage car can suggest many shorter trips for example (not so good)
Service history - has it been served according to schedule and by who (i want to see MB or an MB specialist - not Quick Fit for example)
What other work has been done along the way - especially if there are known weak points on the car you're looking at - eg water pump on the 651 diesel
MoT history and any advisories - have the advisories been rectified and what were they
Are there any big ticket items coming due - eg belts/transmission fluid change etc
What tyres is it wearing - i'll generally walk away if it's got cheap and nasty, or mismatched tyres. Not because of the tyres themselves but it can be an indication a car has been maintained with minimising cost uppermost
Has it had any bodywork done - and by who? I think for Merc to retain the anti perforation warranty it has to be an authorised repair
How long has it been at the dealer? Do the brake discs look corroded suggesting it's been sat a while?
What warranty does it come with - what is covered and what isn't. What is the process for getting warranty work done if needed? Do you have to pay and claim back? You might want to retain a float if that's the case.
I guess they're the main things i check first. I always take a list with me because i know what i'm like! I do a lot of research up front so then i know what i want and what to expect. But it's still very easy to become blinded with excitement when you're in front of a potential purchase with a chunk of cash in your pocket. So the list just pulls me back a bit. To be honest i normally make up my mind in the first couple of minutes and then work through the list to verify.
Hope that helps - happy shopping!