I'll record just about anybody that will let me, as long as there is no PA. Lately I have been recoding a lot of chamber music due to summer chamber music camps occurring now. Lots of string groups ranging from duos up to 100 member string orchestras.
What do I listen for in my recordings? Well, I try to get a good octave to octave balance. What I most often hear is too much treble in the 4kHz to 12kHz range. This is often the fault of SDC mics that have a "bump" in that range. Fortunately, it's easy to eq that bump out. Of course mic placement is important. I try to stay away from the violins for reasons explained below.
I'm also listening for that ideal balance between room and direct sound. What's the ideal balance? Hell, I don't know, but I know it when I hear it. Since I so often record live concerts and do not have a chance to move the mics after the concert begins, I do a lot of MS recording which allows me to adjust the direct and reflected sound ratio a bit after the fact.
Perhaps the hardest thing to do is get the balance between instruments to sound right since I have little control over the musicians placement in a concert setting. In particular, getting the viola to be loud enough is very difficult because in almost every case the viola is on the right with its top surface facing away from the mics, whereas the violin is on the left with its top facing into the mics. In addition, the higher pitch of the violin tends to cut right through the recording, and add to that the afore mentioned common SDC treble "bump" and it can sound like all violin all the time.
So I guess what I am saying is I listen for balance. I don't want any sound to "stick out" in my recording, unless that's the way the musicians played it.