Generally, when a hydraulic tappet begins to rattle on a high mileage engine you might be able to prolong the inevitable and try replacing the oil and adding all your favorite additives. But at some point we have to face the facts and replace what is obviously a worn tappet.
As for the missing O ring causing it to rattle, again, if it's something that has developed over a period of time, and this is on a high mileage engine, it's most likely not a missing O ring. Something like this would reveal itself much earlier in its life, if not within the first 10K miles. In other words, that O ring doesn't suddenly go missing, it's not there from the get go.
It's best to first determine if it's just one tappet or all of them. They generally fail one at a time, however, if they're all noisey this may indicate a problem with the oiling system. Once more, if you have a high mileage engine and you can determine that you only have one or two bad tappets, most likely those tappets are simply ready for replacement due to wear.
To determine if you only have one tappet going bad, find/buy yourself an automotive stethoscope (the one with the long metal rod for probing). With the engine cold and rattling as you describe, carfully probe each cylinder on the intake and exhaust side.
On the exhaust side of each cylinder, touch the probe to the exhaust manifold (careful, it's hot!) as close to the cylinder head as you can. Even touch it to the manifold studs on the head. Those studs act as an extension to your stethoscope and get you closer to what's happening inside.
The intake side is a bit less effective because the M50's plastic manifold sort of dampens the acoustics. Nevertheless, try each cylinder on the intake side as well. Same as the exhaust side, try the intake manifold/cylinder head studs as well; they may give you the best indications of what that cylinder is doing.
You will be able to clearly determine which tappet/tappets are noisy using this method and then only replace what you need to. Lifters from BMW aren't really all that terribly expensive at around $25 each for the M50. So if you can carry out the work yourself, $25 is probably cheaper than all the attempts to prolong its replacement. How much would you spend on mystery additives before you just replaced it anyway?
Dick Schneiders:
Your problem is a bit more serious I fear. You don't have any start up rattle but instead it reveals itself at highway speeds and becomes embarrassingly loud. You need to get this into a shop soon and find out what the problem is. To me, it sounds like the beginning signs of an oil pressure problem. When it's cold you don't hear it because the oil is thicker which of course gives you a bit more oil pressure.
In your case, this may actually be a problem with your oil pump as Bill R hints to. I don't mean to point out the obvious, but this isn't something you can let go for very long before permanent damage occurs.
Regards,
Jake Larsen