A lot of this has been mentioned already, but I'm going to add my $0.02 based on several years of HPDE in an RX-8 and research on how to keep it alive:
Cooling: The stock cooling system on the RX-8 is decent for street, but can use some upgrades for track use. There is a lot of stuff directly behind the radiator (battery, air intake box). If you can clean this up and add hood vents it will help. The coolant overflow tanks can get brittle with age, and a lot of the cheap cars will likely need replacement. I seem to remember reading that rotaries reject ~50% of heat through coolant and ~50% though oil (might have been 60/40). Either way, don't forget the oil coolers. Manual RX-8's in the US have two oil coolers that reject heat into the front wheel wells. Opening up or removing the inner wheel well liner can help airflow. The stock cooling gauge is a dummy gauge. It hits center at ~160 and doesn't move again till 230. By then you are already too hot. Get aftermarket water temperature and oil temperature gauges.
Ignition: The stock ignition system is decent, but the coils do go bad. With mixed street/track use I replaced coils plugs and wires every 15-20K. If you find a car with "low compression and blown apex seals" there is a decent chance that it is just bad coils. For some reason, the coils going bad can cause it to read low compression. Bad coils will also cause the cat to clog, so watch out for that as a possible cheap fix to a "blown engine". Black-Halo-Racing has an upgrade kit to replace the coils. They used to use LS coils, but I think they recently swapped to something else. Most of the research I have done recommends BHR or stock.
Fuel: As mentioned above, you can get fuel starvation at 1/4 tank on long lefthand sweepers. I would add a fuel cell or surge tank if doing endurance racing. I want to say I got 8-9 MPG in a HPDE setting.
OMP/Premix: The Series 1 RX-8's (2004-2008) only had two oil injectors per housing. The Series 2s added the third injector back. I think the stock ECU will go into limp mode if the OMP is unplugged. I kept the stock OMP and add premix on top of it. You can also get the Sohn OMP adapter that allows you to inject clean 2-stroke instead of crankcase oil. Even if you keep the OMP, I would premix an S1 since it is missing the center injector. The OMP doesn't actually pull that much and I think I was using less than 1 qt in 2hrs of track driving.
Clutch pedal: The clutch pedal bracket is a weak spot. They are spot welded and don't have enough lateral support. There are kits out there to add support to the bracket, or you can weld it yourself. If the clutch pedal is squeaking, I would check for cracks.
Brakes: The stock brakes and ABS are really good. The only thing you need to watch out for are "grabby" or "on/off" pads. You want something with some modulation or you need to be smooth upon activation. I was running HP+ and if I got onto the brakes too fast on a cold day it would activate ICE mode on the ABS and you loose braking.
All that being said, they are good cars for track. A lot of the rotary's bad reputation is from people driving it like a Camry, not maintaining it, or trying to up the power without supporting mods. Rotary's are built for track and that is where they excel. The only reasons I stopped tracking my RX-8 and switched to a Miata were cost of consumables and not wanting to tear up the interior for a cage. I am planning on swapping a rotary into my Miata when the stock engine finally dies.