I'm new to the world of the Fazer myself but have ridden Hondas and other Yams for years.
This is what I do...
how many owners overall and how long had the present owner had it. (even if it's a dealer, how long has he had it)
stand back a bit and have a look at the bike as a whole.
Does it look clean, or does it look road weary and grimy in the nooks and crannies
check it's been well kept and maintained,
check the chainis it dry/oily, is the chain ok? does it pull off the rear cog?
do things like the chain adjuster nuts and bar levers look cared for, not rounded or scuffed,
mirrors, are they scratched (sign of a drop) are the hero blobs scuffed or worse missing (sign of a thrashing)
check the tyres are good for a while yet, you don't want to be buying new tyres in two months,
check the service history, look at all receipts for work done and when, five year old work on calipers is well out of date.
check the exhaust for blowing, aftermarket exhausts are normally pattern parts and can come adrift here and there
have a check of the head bearings for notchy-ness
same on the rear wheel bearings
engine, does it start easily from cold, if the dealer has "warmed it up for you" be suspicious of what cold clunks is he hiding.
It's an old bike, how's the gearbox, seat, suspension, lights...
basically look at everything........slowly
and, oddly, does it look straight, literally, stand at the back of the bike and look down its length, does it look straight.
Lastly, take someone else with you, even if they know nothing about bikes as it's a pair of eyes without the rose tints.
If I've missed anything I'm sure someone will be along shortly to correct me.
Do you have a link to the dealers website so we can have a look?