The only real quirk I have had with my LnL AP is the priming system - my specific problem being that with the inertia of the ram going up and down, the primer tube (with the shoulder) would eventually work its way out of the part it sits in that screws to the ram plate. This would cause the primers to no longer stack up on one another and create a hell of a jam inside the shroud. Was a PITA.
I fixed that by JB welding the tube into the part that screws onto the ram plate (obviously had to order another one for the other primer size and do the same thing). Since then, I have not had a problem with the press that wasn't user induced and my priming system works better than anything out there.
Keep a small paint brush (one that would come with a kid's art set - one of those fairly tiny headed ones) to periodically clean out the primer slide area. You will eventually get accumulation there from primer pockets as you run brass through it. If you are using ball powder, it is also inevitable that you'll get a few grains here and there and you'll want to brush everything clean - I usually do this about every 100 rounds, which works out perfect as I'm adding primers at this time anyway. A small can of compressed air is also handy.
Other than that, keep it lubed properly - both the grease zerks on the ram and the occasional dob of grease on the shell plate roller bearings. You should have relatively few problems.
Can't help you on the RCBS die - I just bought the Hornady Powder Cop, and it is simple as hell to use (like another poster, I don't use it on short pistol cartridges - only long ones like .45 Colt and on rifle cartridges).
Like any other machine, it takes a little getting used to at first.