Do bear in mind that some of your old prerecorded tapes may not ever pack that well. When I check a machine I use one of our new tapes to check the pack, and then some old ones that I know are problem children, just so I don't fool myself into thinking every tape will always come out perfect. But all that said, I have been able to get problem machines to pack any tape a lot better than when I first fire them up on the bench, and new tapes can be pretty consistently tight and smooth even at fast wind. I think the reel you saw packing actually had a couple different types of tape spliced together and it still packs really well.
I started on a new one yesterday. Found one thing that seems to be fairly common, which is that the tension rollers are sitting at different distances from the deck plate. That's a good place to start if you're sorting out packing issues. Keeping guides clean makes a big difference too. Any gunk buildup can tilt the tape, and that is guaranteed to throw off the pack.
This is a good time to to mention that if you see a tape that is flange packing, stop. Flange packing is when the tape sits up against one flange, rather than being centered on the reel with some space between the tape pack and each flange. This can curl the edge of the tape and that can permanently screw it up. If it's just one tape that is the problem, experiment with running it onto a different reel, or experiment with applying or removing the silly ass rubber shim for the reel turntable, depending upon which way the tape is shifted on the reel.