It will only immediately cost thousands for a year if you get an SMG and the pump goes
Other than that, don't get rear ended is my biggest advice.
The DSC pressure sensors can fail, get those replaced the moment an error code flags up for them. Leave them and your DSC unit will be next, you don't want that going. There are 2x sensors, a BMW only part at ~£90 each. Replace both ideally as once one raises a flag, it's only a matter of time until the other does too. My car initially flagged up sensor 1, had it replaced and then days later 2 flagged up.
Battery health. Check to make sure the battery is of the correct spec and is healthy. A weak battery will throw up DSC/ABS warnings.
The rear brake lines do corrode over time, though does depend how the car has been kept over the years. The best way to check properly is to drop the fuel tank out.
The wheel speed sensors have been known to get dirty and throw up DSC warning lights.
The famous subframe cracking. Complete lottery on this one, you might have a car that never cracks.. It's all luck with this. £700 to reinforce with ETA Motorsport doing the work using their own fabricated plates.
The exhaust flange brackets that attach the midpipe to the backbox will corrode on every single car with the stock exhaust system installed. You can pay the ~£700 BMW want to replace the mid pipe which has the clamps attached, or cut off the corroded brackets and fit aftermarket stainless steel ones which cost £25 for the whole set (+£8-£10 for the gasket rings from BMW). Guess which option most people choose.
The thermostat will fail at some point, usually around the 70-80k mileage range. I replaced mine as a preventative measure during an oil service. It's not an expensive part really. The water temp needle won't always be dead centre though just to note, it may sit slightly below the middle. This is normal.
Suspension coils will crack every few years, not M3 specific as all E46 with Sport suspension has this issue. You want these replacing in axle pairs.
VANOS seals are known to fail on earlier model years, your garage can check these anyway.
The S54 is very vocal. You'll get acclimated to how it sounds when it's happy and when it's not. You'll also notice when something doesn't sound right. It is grumpy in the mornings, and you don't want to be working the revs beyond 3k until the oil is at full operating temp. Don't go by the lights on the rpm dial unless you've had the lights coded to reflect the actual oil temp.
There isn't anything else that's majorly M3 specific really, everything else is E46 common faults such as door actuator failing (murderous DIY), hedgehog (murderous DIY), window regulator in the case of the convertible and so on. All of those E46 things are cheap fixes, they're just utterly annoying to do. Expect stuff to break, it is a 10yr+ old car after all.
Providing the seats and cabin trim aren't abused, then a simple £150 steering wheel re-trim and gear knob swap (along with gaiters) will result in a cabin transformation. The bolsters will almost certainly be worn on the driver side. You can buy a colourant kit from furniture clinic for £40 which will see that sorted. It seems nobody takes care getting in and out of their cars during ownership!