Moen cartridge moves but won't come out

More than likely lime/calcium build up. I would attempt to "unscrew" it (although there are no threads.) This will help break up the build up inside the body of the faucet. Be firm but not too aggressive. If this doesn't work - squirt a little bit of vinegar or CLR around the barrel. It should soften up enough to remove it.

Jim Mc Namara

Thanks, turns out I just needed to pull harder. Now I've installed the new cartridge and it seems there's a _very_ slow leak around it. Will it tighten up under water pressure over time or do I still have problems??

Sounds like lime in the valve body. Take the cartridge back out and see if the valve body (where the cartridge slides in) is clean and smooth. If you can see deposits, you should try to get rid of them--vinegar or LimeOut, and maybe scrub with a toothbrush.