I've just recently gone through my entire car, after blowing a front main. Inside of the dash, inside of the engine bay, under the car, everything. I replaced the front main seal, valve cover, serpentine belt, water pump (with a metal turbine and housing! Definite upgrade!), cabin air filter, engine air filter, oil change, and reassembled it all. I cranked her over, and had a fairly consistent miss on cyl #4. I reopened the valve cover, and one of the arms fell off of the lifter, so I pulled it, and noticed it was collapsed. Not even after soaking it in ATF, did it come back around. I ordered a new set of 8, and I'll update this thread if that's the fix. Be it known that this could happen to you, and that they're $8/each. If you have to take the valve cover off, you may as well do them if you never have. The rest of them were kind of weak, too.

The car was sitting in climate controlled storage for two years, so that's almost certainly a factor, but it did have a tick beforehand. Just make sure you test them before something catastrophic happens!

 

How many miles on your engine when you noticed this problem?

I've recently put two MINIs (one N16 and one N12) back together. The N16 had a hole in one exhaust valve, and the N12 had 3 dropped valve seats. The N16 had 96K miles and the N12 had 150K miles. There were no issues with the N16's lifters, but I had the exact same problem with the N12, but there's a catch.

On the N12, The repair to the valve seats didn't work, and the seat dropped again after just 10 miles. Since the seat dropped, the valve wouldn't close all the way, and when the camshaft lobe rotated (valve closed position), there was a huge gap between the roller on the rocker arm and the cam lobe. The let the rocker arm fall off the lifter. So if you do see a rocker arm that's fallen off the lifter, it may be the lifter or it may be a dropped valve seat (or both).

Upon closer inspection I found that several lifters on the exhaust side would not compress at all, and every single lifter was not within spec for height (worn out springs). So, I pulled the VANOS spring on the #1 cylinder intake valves, removed the intermediate levers, and then the lifters; both were shot. I spent about $150 to replace all intake and exhaust lifters, It looks like the machine shop got the valve seats right this time, and the engine is running well now.

While shopping at Rock Auto. I clicked on the "info" icon under the Melling brand lifter. Here, I found a spec for the actual lifter height. I was surprised I could not find this spec in BMW's TIS.

For the exhaust the height should be 1.173"



The spec sheet for the intake is 39.40mm (converted properly, error in their spec sheet), it comes out to 1.551" not 0.394" as seen in the sheet below.

 

It was at probably 89-90. I have since put about 20k on the valve seat repair and ran it into a road sign today during a blizzard, so I'm buying parts for that now. The head seems to be holding up just fine, but I must have gotten a bad aftermarket valve cover, because this one is sputtering oil, and giving me a low pressure light. It's going off the road soon, so I'll take some time to investigate how the whole engine has held up since the partial rebuild.