Common problems with the E46 are very similar to those with the E36. However, the E46 has a few unique issues of its own. One of the most well-known issues with the E46 is subframe cracking. While there is nothing inherently wrong with the E46 subframe design, repeated stress can cause a fatigue failure which eventually leads to fractures.
The accumulator is easy to see from there. You're on the right track though as the oil line can really only be seen w/ mirror and light. If you hit a dead end there, you can buy a dye kit ($25) from an auto parts store. You add the dye to the oil, then use a special set of glasses and UV light to inspect.

There is a data port in the area where the clutch pedal is, or would be if you had one, that you connect a scan tool. The scan tool will report various codes that define the reason for the light to be on. SERVICE ENGINE SOON can come on for any of about 400 different reasons, not all of them come from emissions systems.

2000 BMW 328i ; If there's a common sight linked to BMWs, that'll be the appearance of oil stains underneath spots it's been parked in — little wonder it's one of the issues BMW owners keep on T. TxZHP04. 5089 posts · Joined 2006. #2 · Dec 29, 2010 (Edited) If it's an actual vibration and the engine isn't missing (which might indicate a lean misfire or plug/coil issues - with no codes and occurrence within a narrow rpm range, sounds more like a true vibration) then it's either bad mounts or a crankshaft vibration.
1 We Wouldn't Buy One: Subframe And Floor Issues. BMW Blog. Another common issue that will make us shy away from purchasing this car is the rear sub-frame and floor issue. This has been an issue since the E36, which was also carried over to the E46. Via BMWBlog.
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bmw m3 e46 common issues