While most of us are searching for the perfect color combination, there are many other things to look for in an M Coupe. To start, look for a complete set of maintenance records, so you can judge the car's service history and verify its mileage. You should also consider ordering a title report from AutoCheck® or Carfax to verify a clean title and make sure there are no unknown accidents in its history. A Pre-Purchase Inspection by a mechanic knowledgeable of these cars is also a must regardless of the coupe's apparent condition and mileage. Any inspection should include the usual checks for engine compression, cosmetic flaws, body and chassis corrosion, accident damage, malfunctioning accessories, etc.
There are many things specific to the M Coupe that should be checked as well. The list below encompasses most of the common issues you should be aware of and have checked out when looking to purchase an M Coupe. It was originally compiled by wildag (www.dreamingwell.com) in this Bimmerforums thread. I've edited it to be more coupe specific and added a few of my own thoughts. I plan on editing and adding to it as I come across more information.
The water pumps on Z3s fail like clock work around 60k. If the car is over 50k, and hasn't had the water pump replaced, expect to replace it. The usual symptom of a failing pump is a noisy bearing. I highly recommend to upgrading to a water pump with a metal impeller like the one from Stewart. Part costs ~$150 and labor is 2 hours.
Differential Mount and Trunk Floor Welds (Subframe Failure):
This I'm sure is the issue you are probably most aware of. As far as I can tell, the problem is not as widespread as you may have been led to believe, although it could be a significant problem. The issue is commonly referred to as subframe failure which is kind of a misnomer. The Z3's differential mount and rear trunk floor welds are prone to tearing. To inspect, remove the carpet in the trunk and look for spot welds along the back floor. These spot welds should be little flat circles. If they are sunk, or cracked, there will soon be a problem. Under the car, look at the C shaped mount to which the differential is bolted. Inspect for tears in the corners of C. Also look at the bottom of the trunk floor for signs of tearing or separation.
Randy Forbes and Dinan both have kits that strengthen the diff mount and trunk floor. These can be used as a preventative measure. A comparison of the two kits is discussed here. If the coupe you are looking at has been reinforced, it's a really big plus.
A lot more information can be found in this Bimmerforums thread and the Z3Power Website.
Alignment Bushings and Brake Pads:
While driving the car at least 40mph, lightly hold the steering wheel and press the brakes with force. If the car swerves, or does not stop in a smooth straight line, you'll need to inspect the following: front control arm bushings, tie rod bushings, brake pads and rotors. The control arm and tie rod bushings may be cracked or broken, causing extra “play” in the steering alignment. The brake pads and rotors may be too worn or warped.
Rod Bearing Failure (2001-2002 M Coupes):
The S54 engine in 2001-2002 M Coupes had a very significant design flaw that can be fatal to the engine. The rod bearings on the crank shaft can become misaligned, causing the crankshaft to move out of alignment. Replacing these bearings with an updated version is a permanent, but costly fix. All S54 owners should ensure that this problem has been corrected. BMW covered this problem under warranty on other models, and has been known to cover this issue on a case-by-case basis for the Z3. If purchasing an S54-engined M Coupe, check the maintenance records to see if either the bearings or entire engine have been replaced. Expect to pay $800-$1200 to have it done on your own dime.
Manual Transmission Shifting:
The manual transmission shift lever may lean to the right (5th gear) or may be difficult to put in 1st and 2nd gear. This indicates worn shift pins, most often due to excessively aggressive driving or mileage. Replacement parts cost around $100. It could also mean the 5th gear detent needs to be replaced. The transmission needs to be removed and special tools are required for either of these services. BMW does not publish service instructions for the Z3 transmission, so a seasoned transmission specialist will need to be consulted. These issues may sometimes be resolved with a simple fluid flush and change.
Slight Seat Rocking:
With hard acceleration or braking, both the driver's and passenger's seat may rock slightly. This is caused by two very soft rubber bushings that have deteriorated. You can order a fix it kit from Doug Whalen or find one on Ebay. It takes about 3 hours to fix both seats.
Dash and Center Console Lights:
The lights behind the gauge cluster and HVAC controls in the center console may burn out. The lights themselves are very cheap, but replacement can take a few hours.
Check that dash and center console lights are illuminated when the head light knob is pulled out. If they do not illuminate, try turning the head light knob in either direction. If the lights dim heavily when they're supposed to be lit, do not have a consistent slope of illumination or are completely dark, the head light knob circuit needs to be replaced. Parts are about $90 and installation takes an hour.
Check that turning the "hot/cold" HVAC knob (center) has the desired effect. If the knob turns very easily, or not at all, there's a problem with the tension cable. If the knob moves too easily, the HVAC control may need to be replaced for about $150. If the knob doesn't move, especially from hot to cold, the tension cable needs to adjusted; 2 hours of work.
Check that turning the fan speed knob (right) has the desired effect on all 5 settings. If the knob only works on the upper most settings, its likely that a resister in the fan control has broken. Parts cost about $30 and require 2 hours of labor.
Check that the stereo speakers all sound normal. The subwoofer and kick-panel speakers will degrade over time. The subwoofer is very expensive to replace, but there are many aftermarket options. The kick panel speakers can be replaced easily.
Sagging, Squeaky Glovebox:
The glovebox may sag, or not align correctly when closed. This is caused by poor design of the glove box door and latch. This can be fixed for about $20, and 2 hours of work.
Rear Shock Mount Bushings:
The rear shock mount bushings wear quickly in spirited driving. You will hear a solid “clunking” sound inside the cabin from either side of the rear. This indicates that these bushings have worn and need to be replaced. Parts cost ~$30. While Roadster install time is around 2 hours, Coupes require disassembling almost the entire trunk carpet, and therefore takes around 3 hours. I would suggest installing Rouge Engineering Rear Shock Mounts, as they will allow much easier replacement of these bushings in the future.
Parking Brake Cable Tension:
The parking brake cable can stretch over time. This may cause the parking brake to not fully engage, and the cable may rattle against its retainer clips during normal driving. The rattling sound will appear to come from outside the car and over the driver's left shoulder. The cable can be re-tensioned using simple tools; takes about 30 minutes to learn. In some cases, a retaining clip and spring inside the rear wheel hubs may have failed, causing the rattle. These can be replaced for ~$20 and take about 30 minutes.
Uneven Tire Wear:
Moderately uneven tire wear on all four tires is normal. The factory recommended camber and toe setup will cause this uneven wear. Tires that are heavily worn on only on one side of an axle indicate a suspension geometry problem. This may be due to sagging springs, bent arms or NASCAR circuit driving. These kinds of issues can be quite costly, and should be remedied before purchase.
Thanks again to wildag for initially compiling this list and allowing me to post it here. Please let me know if I've missed any other issues that M Coupe shoppers should be aware of in their search.