I just went through a similar issue with my X5. The family complained that it was running like it had water in the gas (this has happened a couple of times to us) so I drove it for a week and it was running fine for me. Gave it back to them and the issues came back about a week later and stayed. It threw a bunch of codes (I wrote them down but I can't find them now) which I cleared and then it threw one code for a bad ignition coil on cylinder 1. I swapped it to cylinder 2, reset the CEL and got a new code for the coil on cylinder 2. I put in a new coil and the issue has been gone since.

I was worried that it was a vacuum leak as well but when I opened the oil fill the vacuum was strong. I had to replace the engine on my X5 and when I did it I missed plugging in the EGR vacuum line and I was getting all kinds of codes for lean cylinder 4. If it works sometimes and not others I am leaning towards it been electrical in nature.

My e36 had a fuel pump go bad and the car was running like it had bad gas too. I replaced the fuel pump with a dealer fresh pump only to have that one go bad 2 weeks later. I though it "it couldn't be the new pump" but after million hours of trouble shooting that is exactly what it was. BMW at least gave me a new pump to replace the bad one but I didn't get paid for my wasted time...... Good Luck!

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2001 3.0 X5 5M - 227k - "Station Wagon according to the great communist state of IL"
1995 M3 5M - 230k and waiting for a new head gasket
1988 325i Auto Convertible - sold
1992 318i 5M Convertible - sold
1992 325i 5M Convertible - sold
2001 330i 5M Convertible - The more money I put in, the better it gets...
1998 K1200RS - Done all 48 Contiguous States, looking forward to Alaska at some point in my life