I'm about to replace the cup-and-cone bottom bracket on a 1982 Bianchi with a cartridge one and I'm looking for advice on re-installation of the right-hand cup. I know that in the "good old days" these tended to loosen due to the effect of precession on the threaded joint, so I'm wondering if, in the intervening 33 years an effective technique has evolved to prevent, or at least minimize, this phenomenon. Any advice would be much appreciated.

RGP

The obvious answer would be threadlocker and if you are worried about disassembly use a low strength product. In Loctite's system that would be purple instead of blue.

The thread direction issue is greatly exaggerated. Consider the millions of bicycles made and sold in Italy and France over the prior century. These aren't exactly countries you'd expect to not understand bicycles.

Also, consider that despite the Right/Left threading of pedals they still unscrew fairly often.

So cups may unscrew regardless of thread direction, though it's possible (or even likely) that the problem is more common with RH threads. The key is to properly install it TIGHT, and if you ride in any kind of weather, with greased threads. RH or LH thread, the real issue isn't loosening, it's getting it of 2 years later.

Is it an issue with cartridge bearings ?

It might be an issue with ANY kind of BB, but it shouldn't be worse with cartridge bearings since the right cup is always installed and tightened first, before the rest of the BB is installed.

Keep in m ind that bicycle BBs were routinely installed both in Italy and England for about a century without any adhesives or special prep, except greased threads and proper torquing.

+1, Get er Tight .. A tool hold down on the BB wrench will allow you to put enough torque on the threads to not come Loose.
tap on the other end of the handle with a Soft faced hammer/ mallet.

Thanks, Guys! I'll clamp the BB wrench tightly with a bar clamp across the frame and LEAN on a two-foot cheater bar. That ought to hold the rascal in place!

RGP

It is possible to overdo this and damage the cup or, more likely, the bb shell's threads. The recommended torque is in the 350 - 450 inch-pound range and that is very tight but not destructively so.

The recommended torque for my Campy Italian threaded bottom bracket is 70 nm, or about 620 inch pounds. And that's quite a-lot.
On the original build it did come loose. But after putting 70 nm on it, it hasn't come loose again. I used my old 1/2" beam torque wrench.

BITD, before people published torque specs, we tightened the hell out of them, as in let's get this so tight it won't ever come apart. Crapshoot guess, we were going well above 60-70 foot pounds. That was back when everything was steel.

I don't believe it's possible to strip a frame or cup from over-tightening, even with aluminum, but I have seen ham fisted mechanics crack the flange off aluminum right cups, so some common sense is still called for.