One of the things I see many beginning engineers do that causes problems involves the placement of microphones. On guitars, amps, drums, vocals, everything.
When placing a microphone, you should consider the microphone's pickup pattern (omni, cardioid, etc), whether it has a proximity effect, and what sort of sound you're after.
Generally, in rock, we think of most sources being close-mic'd. That is, we place the SM57 just in front of the speaker grill, closer if we can get it! The same logic is used on drums, with close micing, the vocals, and the bass DI'd. While these may make sense in theory, you rarely get the best tones solely by close micing, and in many cases, you overpower the mic so that you're adding distortion.
My general technique for micing a guitar cabinet is to start about a foot away, with the mic pointing directly at the speaker. Listen to the signal and move back or closer to get a fuller or thinner sound. Contrary to logic, you get a fuller, meetier sound by moving away. This is because bass frequencies have longer wavelengths, and require more air to develop. Proximity effects counteract this somewhat, so some experimentation is necessary.
If the signal is weak, try turning the amp up. Listen to the amp with your ears plugged. You should be able to get a sense for the type of distortion coming from the amp. Whether it's overdrive or speaker breakup, a distortion pedal, etc, they all have distinctive sounds.
Now, listen to the signal coming through your monitors. It should have the same distortion, but no more. If you're hearing high end distortion that wasn't there at the amp, you need to move the mic back farther, or turn down the amp. You're likely overdriving the mic.
With bass amps, it's the same theory. I usually use a Large Diaphragm Condenser, about 3ft back from the cabinet. You have to listen carefully for distortion, it's easy to overdrive a mic with loud bass. Move in or out to get more presence and bass.
Drums are a whole other game. There's no easy way to mic a tom without getting right on top of it, if you want any degree of isolation. Adjust your tom and snare mics to get the best tone, watching to avoid overdriving the mics. If you're using condensers, be sure the pad is switched in. Dynamics are more resistant to being overdriven, which is a large part of their popularity for this application.
The kick drum, on the other hand, does require some experimentation, and because of it's location, you have a lot more freedom. You'll find that as you get closer to the kick head, you get more attack, more "boing" from the head itself. Moving away, as far as several feet outside the head gets you more bass and more sustain. Many engineers prefer to mic both, which gets you a full spectrum to work with. Be careful to check phase though.
Overheads are another place where you have lots of room to experiment. I won't go into too much detail, but keep in mind that the farther you get above or in front of the kit, the more reverberant the tone will be, and the more you will hear the room tone. If the room is good sounding, go with it. If it's not, get the overhead mics in close.
For vocals, you often need to have the mic a few inches back from the pop screen. Experiment with different distances, as the proximity effect of cardioid mics can have a big impact of the tone of the vocal track.
Room mics are another big part of the equation. I like to use room mics during tracking, to get the sound of the whole band on one track, which can be compressed, eq'd, etc. This way you can make the room more of the mix or less of the mix, to emphasize different parts of the song, or just get the right feel.
With vocalists, I'll often set up a room mic during their overdubs. Mixing a little of this natural room sound in can help glue the vocals to the rest of the backing tracks, helping them fit in the same "space".
Generally, you should experiment with mic placement, by starting as close as you might imagine is practical, then moving farther away. I've tracked acoustic guitars from 10 ft with great effect, backing vocals from 15 ft, and drums from across the room. Walk around and listen with your ears. If you find a spot where things sound great, stick a mic up.
Expensive mics and gear provide some of the colors on the audio engineer's pallet, but simple things like mic placement can provide more variation than you might imagine.