This is an ongoing problem with hot water in my shower and tub. Whenever we try to shower, it takes forever to get hot water into the shower. After a while if you jam the single handle all the way to the hot water position, you will get hot water on and off. After a few minutes that water needs to be adjusted every few seconds because it gets hotter and hotter. I told my landlord about it and he came and check ed and said the water jacket in the furnace needed to be cleaned out! All of the other hot water faucets are fine. After spending a few hours cleaning the jacket out in the boiler, he also changed the cartridge in the shower faucet. It still does not work properly. Now I have been doing bathroom renovations and plumbing for a lot of years and I told the landlord that the brass body of the shower faucet is bad. He does not understand that after 25 years of expansion and contraction, the brass has weakened enough that it just will not seal the cartridge properly. I have seen it before and had to change the entire faucet. Assembly and valve. Should I just take it upon myself to change it or just put up with cold/scorching showers?

after 25 years of expansion and contraction
Never heard of that, nor does it account for fluctuating mixture of hot and cold.

What makes more sense is a faulty mixing valve on the boiler.

But every other hot water faucet is fine,, no fluctuations at all.

Even the sink right next to the shower/tub is fine.

When replacing the cartridge was the valve flushed. Possible debris in the valve trapped by the cartridge.