Well, every Mac originally came with a "Hardware Test" disc--on older computers it was a separate disc, on newer ones you get into it from the system restore disc by turning on the computer with the disc inserted and a certain key held down (it'll say on the disc). You can use that to run a moderately thorough hardware scan, which won't find EVERY problem, but will generally give you an error if something is obviously broken or malfunctioning.
Doing the "long" test runs a more thorough test of the RAM, which can take quite a while (an hour or more on systems with a lot of RAM), so keep that in mind.
Can't remember if the G5s of that vintage had a separate disc or not, but if the seller has the discs that came with it you should be able to figure it out quickly enough, and run that before committing to buy.
Otherwise it's just the obvious stuff--make sure it boots, open a couple of programs to see if everything seems ok. You can open Disk Utility and check if the hard drives are reporting their SMART status as ok, but the hardware test should also check that.
Incidentally, many people sell Macs with lots of stuff--like Office and Final Cut Studio--preinstalled, but they're not actually giving you the installation media and serial numbers for those applications, so it's essentially the same as a bootleg copy (or literally a bootleg, if they don't even own the apps themselves and just downloaded a pirated copy). It's worth checking that if you want to be on the up-and-up, considering that FCS 2 and Office 2008 would cost you around $550 if you bought legit copies by themselves, which is significantly more than the value of a Dual 1.8 G5 tower--I just sold my dual 2.0 G5 with a few hardware upgrades for $500, and that was a very good price.
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