Oh my god, i can relate! I suck at remembering certain things, but then there will be other things that i remember in detail when no-one else around does. It takes me awhile to catch on to someone's name. There have been multiple times where someone will be talking about someone else where i work, and i'll ask "uhhh, who is _______?" And it'll end up being someone who's been working there just as long as i have, who i've seen over and over again, just never remembered their name. Birthdays i also have problems with, and remember how old someone is(i mean, it changes every year! lol). But then again, i might remember the name of some obscure disease or something that no one else really thought to take note of. I think it might depend on how much whatever it is interests you, or whether or not it makes you think about it. Like, if i hear something and it reminds me of something else, then thinking about it like that kind of makes a mental note in my mind... whereas something like a name usually doesn't make me think of anything in particular, so my mind doesn't register it.
On the whole face thing.. I'm not as bad as some people with that, because if i see someone a lot then their face will form a really clear image in my head and i'll remember it really well. But with people i don't see a lot, i'm horrible. Maybe it's just because i don't look at peoples' faces all that much, especially those i don't know. But, someone at work might be asking me to get a tv for them, and a lot of the time when i bring it out, i'll completely forget who asked me about to get it. A few times i've even just asked random customers "was i getting a tv for you?" haha.