So what do you consider the most important things to check out on a used boat before you buy it?
Go!

drive it before you buy it .will save a lot of misery down the road.

Does it have a Clear-Title. In hand.

Condition of boat overall
Compression or better yet a leakdown of motor
test trolling motor
check steering for proper function
check gauges for proper function
condition of prop and skeg(can tell you a lot about care taken in usage)
check condition of trailer bunks
trailer tire inspection
condition of trailer overall
check hull bottom for scratches and dings
check batteries and terminals for cleanliness and voltage and age
check grease in lower unit for water intrusion
Ask as many questions as you can think of on maintenance before ever going to look at it because if they didn't maintain it well it will normally come back to haunt you.
When was the last time it had an impellar changed
clear title in their name
And if you aren't comfortable doing all this take it to a reputable dealer and have them check the whole boat out. It would be money well spent.

Yep, title issues trump everything up front. If they are in order, I would say transom and floor check, compression check on motor, and if it has a tube trailer, check for rust. Do not buy a boat you cannot do an on lake demo.

clear title *in their name* is a big one.

Up here, especially w/ cars and trucks, lots of fly by night guys "title jump" and the title is still in the previous owner's name, they're just flipping it, then they sign it over to you. if they are evading taxes, that's bad but that's on them - but if they're lying about the ownership history of the boat, you can bet they're lying about the maintenance history of the boat and they probably bought it from a dubious place to begin with.

Stress Cracks in the transom.
Motor...Depending on how old it is, the owner can or cannot fudge on the hours on the boat.
electronics...Do they all work? If not, why not.
TM, Shaft straight?
Boat and Trailer Lights. Not that hard to fix, but could be a harbinger of things to come.
Fuel Lines, are they the new Ethanol Resistant lines. You can tell by the red stripe on them or lack of.