When I bought my M3, it needed a lot of deferred maintenance. Deferred means that the previous owner put off doing work, either out of laziness or lack of interest. Time constraints meant that I had to address certain issues ahead of others. But any maintenance work on the E46 M3 should be done as part of a larger overall service plan.
First, you have to decide if you can afford to put maintenance items into the car. If you add smoked turn signals but ignore the stuck thermostat, this probably isn't the car for you because problems will snowball into repairs that could run up into the high 4 or even 5 digits. Be fair to yourself, the car, and the next owner. But where to put the maintenance dollars?
This S54 engine is basically a race engine. What's that mean exactly? It's built with materials and tolerances that 1) produce as much horsepower as possible, 2) is still street legal, and 3) is moderately reliable. Life expectency is a distant fourth because race engines give up their lives to produce all that power. And periodic engine rebuilds are just expected to continue making all that power. Back in the original E30 M3 days, we recommended complete engine rebuilds every 75,000 miles. In our Grand-Am racing days with the E46 M3, we would dyno the racecars after every race and replaced engines every 3-4 races (and those engines were pretty much stock). It's not outrageous to suggest that a street S54 would benefit from a rebuild every 125,000 miles. With anything more than that being borrowed time. And that's under a best-case scenario with regular full services factored in. Without regular servicing, the engine is compensating and this would show up as low power, poor fuel economy, high(er) oil consumption, and MIL/SES lights and warnings. The problems may be internal and go un-noticed until one catastrophic failure sidelines you and the car. You're not going to know that there's a problem unless you get in there to perform the recommended service work.
All right enough pontificating. What is the recommended service work for the E46 M3? Here is the maintenance guide generally followed at Turner (E46 M3 Maintenance Package):
Annual Maintenance - air filter cleaning or replacement, MAF sensor cleaning, cabin filter replacement, fluid top off and bleeding, leak check and diagnosis, suspension ball joint and bushing inspection, and brake wear check.
5,000 mile oil change intervals - oil, filter, seals, o-rings. Maybe every fourth or fifth oil change, send the oil out for analysis. This is a good indicator of how much internal wear is taking place.
30,000 mile service - engine oil change, air filter replacement, transmission and diff fluid changes, fuel filter replacement, drive belt replacement, and the items listed under annual maintenance.
60,000 mile service - everything from the 30k service plus: valve adjustment with valve cover gaskets, spark plugs, ignition coils (possibly), and inspect cam sprockets for cracks.
The above items are considered part of BMW's Inspection I and Inspection II maintenance programs. Of course, there are other parts on the car that are subject to regular wear and tear and you should also plan accordingly for their replacement. A lot depends on how and where you drive but you can consider these guidelines for the rest of the car -
Brakes - pads every 30,00 miles, rotors every 60,000 miles. Replace brake fluid every 1-2 years.
Front Suspension - bushings every 40,000 miles, control arm ball joints every 60-80,000 miles. The bushings can be evaluated by visual inspection but replace the control arms based on mileage. The ball joints may be worn without a visual or feedback showing while driving. Strut mounts last a long time but the separate bearings should be replaced every 70-80,000 miles.
Rear Suspension - trailing arm bushings every 50,000 miles (when not used with Turner Bushing Limiters). Shock mounts every 40-50,000 miles if you're only using the stock mounts. Other rear bushings can be replaced based on visual inspection but should last a long time (>80,000 miles). If you have a clunk in the rear suspension, that is different than the normal muted diff clunk, have the rear subframe and floor inspected immediately.
Tires - there are too many variables here to give an indication. After 10,000 miles inspect upon every oil change.
Battery - every five years. Use an OE BMW or Interstate battery.
Cooling System - the E46 M3's water pump and radiator are tried and true and not subject to the problems on past US E36 M3s. But I complete overhaul by 85-100k miles will ensure you are not let down by a preventable cooling system failure. Replace the whole system - water pump, thermostat, hoses, radiator, and sensors. And use the BMW coolant of course. Here's a cooling system overhaul package: http://www.turnermotorsport.com/p-2162-complete-cooling-system-overhaul-package-2001-2006-e46-m3.aspx
Clutch - this also depends on how you drive or treat the clutch. Under normal "M3 use" I would expect to get 80-100k miles from a stock clutch. But don't assume that the previous owner(s) treated the clutch as well as you do. The guibo and center support bearing of the driveshaft take a lot of strain as well so expect to replace those every 40-50,000 miles (especially for the guibo). We replaced transmissions several times a season when we raced these, even with oil coolers. A street car driven correctly should not really have to suffer this but tracked cars certainly may. There's also a cv-joint where the driveshaft meets the differential that wears out frequently. Unlike a u-joints, this can be replaced on its own with the driveshaft still in the car.
Of course, there are other components that are subject to wear and will need periodic or regular replacement. But consider this a general guide to common E46 M3 maintenance issues and you should have no problem enjoying your M3 for a very long time. The important thing to remember is that if you're not involved in the maintenance of your car, you really have no idea if critical components are about to fail or are holding up well. And also remember to have fun with the work you do.