Something I was been made aware of recently, was a loose fuel injector (leaking air) on a BMW 650, caused no end of grief here with our dealer/distributors. So if your 650 is a bit hairy, best we all check and make sure our injectors are tight and not leaking air as the BMW was.
Parts 9-14 are the injector assembly and are located just beneath the lower half of the air box. Check the "o" ring part #12 for a good seal and look for cracks, Check part #14 the cir clip to insure it is seated properly and of course the bolts #10. As long as you are there check the hose clamps Parts # 15 for tightness
Can you use the old trick with carburetor cleaner to see if the idle picks up if you spray around it?
I have done the test with brake cleaner (same ingredients such as carburetor cleaner) and found no leak. Neither at the injector, nor at the rest of the injection system. Everything tight