Window regulators - seems to be the most common issue with 2003-2010 Vipers. Replacing both will cost you about $2,000 in parts alone, so make sure the windows both work well (no crunching noises, etc.).
Some 2008 owners have had issues with the side glass breaking unexpectedly - there was a bad batch of glass that made it into some cars. From what I can tell, there's no real way to tell whether or not it will happen to yours. I'm the second owner of mine, but I don't think the previous owner had this issue, and it's been fine since the day I brought it home.
Oil cooler lines - these are a fairly common problem. The factory design seems prone to leakage - aftermarket replacements are available, but it isn't the easiest install in the world as I found out about a month or so ago. Not a huge deal, but see if you can get eyes on both ends of the lines (at the oil cooler near the passenger side headlight and underneath at the block) to see if they are leaking. Mine started leaking a little, so I replaced them both.
Expect some transmission gear rattle at idle in neutral - it is perfectly normal for these cars.
People also complain about throttle lag - it isn't great, but it isn't horrible either. It's a function of the drive-by-wire throttle bodies introduced in 2008.
Some complain of jerkyness at low speeds. This one is a simple fix - don't drive it slowly. Parking lots should be taken at 100+ MPH, no exceptions. But seriously, if it starts bucking on you during slow maneuvering, just push the clutch in.