I just purchased a 540i auto, my second e34. I got a rough history of the car, but very few records so it is hard to tell what has been maintained.

I have done a search through the threads and have some ideas about what might be the cause of the problem, but wanted to get an idea of what to do first.

The problem: heavy vibrations at idle, O2 sensor code.

My question: What are some good ways to diagnose this without running out and buying a bunch of expensive parts?

so far I have taken the covers off to check for oil around the plugs. There was just a small amount toward the rear. The rest looks dry. I guess I should take the plugs out to see how they look. I believe they were replaced within the last few years / 40k miles but theres no way to know for sure.

I'd like to check for leaks. Does anyone have a diagram or can explain where to look for vacuum leaks?

Thanks in advance.