Play in the steering, as noted, comes from many places including the box.
I had more play than I was comfy with in my coupe until recently, and some other noises happening when I did a left hand turn. Finally I got the car up on stands and started shaking things... lo and behold the center tie rod was worn badly at two of the joints (idler and pitman arms if you must know).
This is a large surprise to me since I'd replaced it some years ago and don't drive the coupe all that much. Of course, the odo is out so I can't estimate the mileage for certain, but it would seem like less than 20,000 miles.
Anyway, they're getting harder to find - my FLAP couldn't get one from either of their two wholesalers, SSF and (someone else). A quick net search found the best prices at getbmwparts.com. No affiliation, just that they had the genuine article at a better price, delivered to me in the middle of the Pacific, than other suppliers.
So I put it in, and the looseness was gone but the bup-bup-bup on left handers remains. Very disappointing and food for a different thread.
Where to look: only after securely supporting the car, get under and shake the center tie rod. Look for play at (in L-R order) the left outer tie rod joint, left inner tie rod joint, pitman arm, idler arm, and right inner tie rod joint, right outer tie rod joint. Next the ball joint at the outer end of each lower control arm (note the ball joint is not separable from the knuckle, you have to buy the arm with the joint complete). Check that the bushing on the idler arm is not worn out.
Car back on ground, wheels straight ahead. Check the condition of the steering column u-joint upstream of the steering box, it should not rotate independently of the upper or lower section of the steering shaft. Gently rotate the steering wheel, at the rim there should be maybe an inch of rotation before the pitman arm rotates. (This is the main but not only test of the adjustment of the box). You can adjust the box using the set screw and lock nut on the top but they are something awkward to get at. Every 2002 I've ever had (maybe 15 or so) needed some adjustment and was a happier drive after doing it.
As cautioned above don't overdo the adjustment. Not certain why all the cautions noted above for a simple thing, but I respect those opinions. I have no certainty of your mechanical aptitude or "feel" for the works, so if you're the checkbook type of car-fixer, it's time to get the check out and write it to the trusted party of your choice.