Regarding room treatment for recording vs. mixing: it is, of course, essential for both, and yes, you need different kinds of treatment for ideal situations of either. However, most people don't have commercial studio facilities of their very own, and are therefor relegated to using a single room at home for all their music creation needs. This is perfectly fine, and while it's tough to get good results with a terrible-sounding room, you can have a room that's a compromise for recording vs. mixing and get very good results.
As Pete said, a drier room is better for recording, and for most of us this should probably be the priority. It certainly is for me, anyway, since I make a large portion of my living with remote recording sessions, tracking saxophones, flute, clarinet, and keyboards. So that means absorption: bookshelves, furniture, carpeting/rugs, and acoustic panels hung on the walls help with that. I don't like to deaden the room completely since that tends to suck out all the high frequencies and leaves a rather dull sound, but I like to have enough absorption and diffusion so that whatever room sound is picked up is pleasant and at least somewhat intentional.
A room like mine isn't as ideal as possible for mixing, but there are plenty of workarounds for that. First of all, just knowing that it isn't ideal is important, so I make sure to check mixes on other sources: headphones, car, even laptop speakers. If I can get a mix sounding good in all of those, I'm reasonably sure it will translate well to most listeners' devices.
Second, mix at low volume levels! The best mixing engineers in the world do this. They might have incredibly fancy systems at their disposal, but they might use 5% of its volume capability most of the time. Mixing at low volume levels is good practice anyway, but it's especially important in a room that isn't tuned specifically for mixing. You can get a lot of good work done this way.