A good audio recording of your playing is a great practice tool. Everton Gloeden, from the Brazilian Guitar Quartet, once told me he thought it helped him so much he believed practicing without recording was a waste of his time!
But how do we do it? It depends on what you want to get out of it.
A simple way of starting off is playing through the music once, and then listening until something catches your ear. Pause the playback and work out that section, then move on. Don't dismiss any problem as a mere accident. If it really was just that, you won't spend much time working on it. Also, don't worry about sections that sound good in the recording, but that you've labeled as difficult in your mind. Use the recording as a reality check. Play slowly enough that you won't dismiss problems because it's so fast, or miss hearing them because it's too fast to notice.
What to listen for?
Little loops - when you go back and play something again, wether there was a problem or not
Noises - buzzes, rattles, squeaks
Incomplete chords - you're going through the trouble of fretting and plucking 5 or 6 string, make sure the listener gets to hear all the notes!
Check the rhythms and the pulse.
Long notes and rests - don't cheat them and skip ahead
Another approach is more positive - listen for qualities you LIKE in the recording, such a specially nice tone, a clean fast run, a well-proportioned rubato. Then pause the playback, and study the score for similar passages and spread the love - make sure the they all share those good qualities.
Remember these recordings are for your use only. Don't think of them as recording sessions. If you start to get "microphone nerves," I find it can be helpful to promise yourself you'll erase the recording at the end of the session.