revs bouncing when I try to hold low revs

My BMW 325i behaves oddly - the idle is completely smooth, the engine behaves completely normally at speed, but when I finish a drive and do something slow (reverse park, etc), the revs tank and surge when I try to hold low throttle.

I have checked for vacuum leaks and there are none, and I have replaced the idle control valve, spark plugs, and battery - is there anything else I can check? It has done 85,000 miles, for the record.

Thanks.

What year is your BMW? You mention you checked for vacuum leaks - what method did you use? Also, did you check on a cold engine or in the condition when the slow speed idle becomes an issue? Since you don't mention the year I don't know if you have an electronic throttle or cable driven with TPS. Since you mention and idle control valve I'm going to guess it's cable driven. Have you checked the TPS for linearity?

When you pulled the spark plugs did you compare the look of the portion inside the combustion chamber to see if any looked cleaner or darker than the others?

Do you have access to a scan tool so you can check for pending misfire codes, monitor the fuel trims, IAT sensor readings and ECT sensor readings when the engine is running fine versus running less fine?

-Rod

What year is your BMW? You mention you checked for vacuum leaks - what method did you use? Also, did you check on a cold engine or in the condition when the slow speed idle becomes an issue? Since you don't mention the year I don't know if you have an electronic throttle or cable driven with TPS. Since you mention and idle control valve I'm going to guess it's cable driven. Have you checked the TPS for linearity?

When you pulled the spark plugs did you compare the look of the portion inside the combustion chamber to see if any looked cleaner or darker than the others?

Do you have access to a scan tool so you can check for pending misfire codes, monitor the fuel trims, IAT sensor readings and ECT sensor readings when the engine is running fine versus running less fine?

-Rod

It's a 2001 with electronic throttle body; I have already secured a replacement, which I'll install over the weekend. I can also get hold of the pedal, if need be.

I checked the vacuum with a home-made smoke tester on a cold engine; haven't tested a warm one because the issue happens at all engine temps.

The plugs were all comparable, though a couple had a bit of oil on them (the ones furthest from the breather end of the valve cover).

I use a Bluetooth scan tool that only showed one code - failed post-cat oxygen sensor - which doesn't even show up as an EML. Fuel trims are bang on zero at idle, but increase to around +6 at cruise. (The UK has recently changed to E10 fuel, though, so this might account for it.)

I would fix the post cat 02 before I would spend hours trying to chase another possible issue. If a DTC is set, always repair before looking for other possible causes.