I've been curious about this for a while, and I'm especially wondering because my band is about to put out our next album. Last time we let the same guy do everything: record, mix and master. I personally thought it would be better to get a second pair of ears on it for the mastering portion, but we couldn't afford it. It did not come out bad by any means, but there were a few aspects of the sound that we weren't 100% happy with (bass drum/toms not as audible as we would like in certain sections, various aspects of the guitar tone, etc.). So I want to know what y'all's thoughts are on this, as well as what your experiences are with getting other people to record, mix and master your music?

It's better to have the same person or people produce and engineer the record from start to finish if possible, provided that they have the skills and ears necessary for the task. If the guy who engineers and mixes the record isn't good at mastering, then you should get someone else. Getting another person to do the mastering isn't going to fix balance problems introduced in the mixing stage, or sound problems in general. If anything, it sounds like you need to look for a different person to produce, engineer and mix your next record, and possibly have that new, more suitable person master it as well.

Take this with a grain of salt or two, because I'm still just an amateur.

It's a common practice to send your final mixdowns off to a separate facility and mastering engineer to finish the job and produce the final master stereo recordings. That isn't an issue.

You can also record your parts and have them mixed by another studio as well, but that usually presents additional problems if you're not very experienced with recording your own material and preparing mixdown stems for another engineer to use. Generally though the best practice is to have them recorded and mixed in the same studio by the same people.

I would say that it's best to keep recording and mixing together, as the engineer would have the freedom to make specific choices during recording, knowing he will be the one mixing the material later.
Having a different person doing the mastering can certainly be beneficial, but it's not necessarily a bad thing if it's done by the mixing guy, as long as he knows what he's doing. It's a case by case thing, really. If you do hire someone else for mastering, make sure to work with an actual mastering engineer, who's a specialist in this particular task.

But if you're frustrated with some elements being inaudible, the issue is most probably related to mixing, and should be fixed there.

For Spirit Division's first two albums, we basically had the guys who engineered and mixed also do the mastering. The first one was a happenstance decision and the second was out of financial necessity, but it turned out pretty good both times. For our upcoming album, we spread out responsibilities as our guitarist did most of the engineering, a friend in another band did the drum tracking and mixing, and we sent off to another place for mastering. I'm not sure which way has been the most right so far but I like it best when multiple ears are involved, if only for the personal reassurance.

I would say the biggest issue is working with someone who knows the music you are playing enough to be able to get what you want without you having to constantly go back and forth with the person. The longer it takes, the more frustrated you could become with the recording. I've been recording, mixing, and mastering my own bands stuff for the last two years and while it's taken a while to get the hang of it I feel it eliminates the other person having to do it for me and my bandmates and I waiting for them to get it done.

I would say having someone professionally master an album is the most important because a master can take a good album to great. Especially if you plan on doing it on vinyl or pro-tape.