It all depends on where your comfort level is. Spyders come with a two year transferable warranty so any 2008 or 2009 and some 2010 models may be out of warranty unless the owner purchased an extended warranty. I mention this only because the Spyder is a complex machine and can be difficult and costly to repair. If you're comfortable fixing your vehicles this may not be as big of a concern as someone who has little or no such skills. Still, even for skilled DIY'ers the Spyder can be a handful to fix especially since some repairs require diagnostic equipment not available to owners. If you buy from a private party make sure there is a decent dealer you can take it to if necessary.
That said you can save a lot of money buying used. Try to find one still under warranty if possible. If you buy from a dealer ask for a 30-90 day warranty. At least if it has any existing problems you'll probably know by then. If you buy from a private party pay a nearby BRP dealer about $100 to check it over before you buy. Most people will agree to this, if not walk away.
When buying used first look it over stem to stern. You can usually tell a lot just from its overall condition. Look at the body panels, they should be smooth, even, and well attached. The exterior finish should be in reasonable shape for its age. Make sure you're ok with any flaws. Look for signs of UV or weather damage. Ask where and how it was stored on and off season. The seat should be in good shape, no rips or seam splits. Check the front and rear fenders. They should be well attached.
Ask the owner/dealer to start it. It should start right up. No excessive smoke should visible from the exhaust (steam is ok). When it's running turn the handlebars right and left. It should turn smoothly with a notable feeling of steering assist. Listen carefully to the engine, it should sound steady with no rattles or unusual noises. Slowly roll the throttle to about 4000 RPM (in neutral, with e-brake on). It should accelerate smoothly, then return to a steady idle. Check the dash console for any error codes, there should be none. Turn off the engine, it should stop immediately. Check all the lighting and electricals. Check the front tires for uneven wear. Sit on the seat and rock it back and forth. Listen for any suspension clunking. Work the rear suspension, again check for smooth operation and no odd noises. Look at the exhaust, it should not look burnt, rusted, or carboned up. Look at the drive belt, it should be free of cracks and cuts.
Look for any signs of abuse, bald tires, worn steering, dirty or leaking fluids, signs of an accident, etc. Some people take great care of their vehicles, others trash them. Look for one that was lovingly cared for and you'll be much happier. Next look at any modifications. Mods can be both good or bad depending on the skills of the person who installed them. Ask for a complete list of mods and make sure you are ok with them. Some mods may void the warranty. Ask if the original OEM parts are still available. Check the mileage but be aware that the mileage shown on the dash console my not be accurate if the console unit was ever replaced. A dealer can determine the actual mileage which is stored in the ECU.
Ask if you can test ride it. Some owners/dealers may let you others may not. Don't hold it against them if they don't, this is not a car. A test ride can tell you a lot if you can get one. If you can't then insist for ride as a passenger (bring your own helmet and gear). During the ride listen to and feel the engine. It should be smooth and powerful. A little coughing/popping is normal for some Spyders during deceleration and certain RPM ranges but it should transitory and not be excessive. Listen to the shifting, if anything sounds or feels strange be wary although the the shifting skills of the driver can make a big difference. Also be aware that the semi-automatic does normally clunk loudly when put into 1st gear from neutral. Braking should be smooth and quick. The suspension should be effective with no odd noises. If you're not use to riding on a Spyder expect it to roll side to side a bit during cornering, that's normal and takes some getting used to.
Ask to see the Spyder's maintenance records, the oil/filter(s) should have been changed roughly every 3000 miles. If over 10,000-14,000 miles ask to see a record of the valve clearance check. Look for excessive problems if listed. Ask if all recalls have been done, double check this with the dealer.
Finally ask the owner for an honest assessment of the Spyder. Ask why it's being sold. You'll have to be a good judge of character to get an accurate read.
Do your homework on the price. Look at both the NADA retail value and check eBay and Craigslist to see what the going prices of used Spyders are locally and nationally. Adjust for the condition of the Spyder and for the modifications.
If I missed anything others will fill in.
Many people are willing to take a risk and buy used to save a lot of money. Others are willing to pay more for new. Again it comes down to your comfort level. Best of luck in whatever you decide.