Recently, I had to replace a seized Moen shower cartridge. In removing the old one, the brass piece the cartridge sits in was scored by a drill. It now leaks cold water when I turn on the faucet. What can I do to this brass piece to smooth it out to stop the leaking?
Nightmare. DO NOT attempt to "fill it" as in some other answers, that will just make it worse.
The issue here is that you cannot polish, because it will not be flat in that case. It is absolutely essential that it be flat. You need to indicate exactly where the scratch is. Here is the assembly I think you are talking about:
Is this the correct assembly? If so, where is the scratch?
In general, what you have to do is make a mating part, basically a tube, that fits perfectly flat against seat to be ground. The tube end has to sanded absolutely flat using a pane of glass, for example. Then using either a loose abrasive or a ring of sandpaper about 600 grit you turn the tube against the seat and gradually grind out the scratch. Its time consuming.
You may want to consider replacing the whole part. Depends how much you value your time.
I wonder if some Bondic could help here.
I've never used the stuff, but I've heard the only real downside is that UV exposure can degrade it over time, which isn't a problem inside a plumbing fixture.
See http://notaglue.com/ and I'd be interested in anyone else's experiences with this stuff in this sort of application.