early cars:
Built before spring 2013 - bad factory tune that could result in knock under hard driving destroying the direct inejector seals
Fix - Updated factory tune or aftermarket tune, if seals are damaged direct injector seals need to be replaced to prevent further knock and potential loss of engine
Failing coil packs - heat/sustained high rpms associated with tracking will cause the coilpack to fail, results in some minor misfire on track, engine throttles back, check engine light comes on, can be ignored for a bit. Coil packs are ~$80 each last I checked, annoying to get to but not impossible, 10mm bolt and a harness plug iirc. Hardcore track, you could be replacing one every 3-4 events.
Fix - CSG posits updating to 15+ wiring harness and coilpacks (connectors changed for '15+), maybe updated coilpack part numbers are more durable, not sure as I haven't taken my car back to the track since getting the updated part numbers and nobody else is talking about 'em.
Those are the track specific issues I'm aware of, there are a few more issues that are hit or miss related to the early cars. I'd bargain that an car with reasonable street miles would have exhibited symptoms of the following already and risk is low on the issue popping up now. Could be wrong though. I wouldn't buy a babied '13, it should have tens of thousands of miles and have seen redline more than a few times.
Leaky Timing cover or other joints - oil seeps around sloppy sealant
Fix - remove leaky part, re-apply sealant, cross fingers
Variable Camshaft Timing - Few things went funky here, sensor assembly tolerances, oil passageway on cam gear popping off, oil control valve clogging, ecu getting 'burned into' the wrong advance value from one of the prior issues
Throwout bearing - wears out prematurely, sometimes
Valve rockers - poorly crimped from the factory a few failed and popped off, shooting a valve through the valve cover
Sloppy sealant from the factory could clog coolant or oiling passages resulting in overheating, VVT problems (above) and even spun bearings from lack of proper oiling to #4
Note that oil temps are high enough to cause concern, most vendors recommend oil cooler as such.
Read through the list of TSB's if none of them scare you imho the only big things are the first two, injector seals getting damaged could lead to a blown engine and eating an extra $80 every couple track days gets old fast.
http://www.ft86club.com/forums/showthread.php?t=21868
The chirping noise from the fuel pump is overblown and not indicative of anything wrong, it's just noisy.