Is it possible to use old worn-out drum batter heads as resonant heads? I have a couple of heads that have dents in them, and are sounding pretty crap, and I'm wondering if it's worth using them as resonant heads, when those wear out. Will the dents reduce the resonance quality? If so, in what way?
I would advise against doing so.
I expect that you intend to exchange both heads of your drum, to save some money. I've done that, once or twice, because I had to (very bad dent on the batter head, no spare available, and I had to play).
First, it supposes that you use the same model head on both sides of you toms, which is often seen but in no way a requirement. If you have different weights on both sides, you will get a very different sound.
Second, if you think that the batter head has a crappy sound, chances are the head is worn, and you will find it difficult to tune your tom to get a nice sounding sound, with that head on the resonnant side: the batter head suffers from higher physical stress, and a worn batter head is often more stretched that its resonnant counterpart.
Finally, your tom might not be perfectly built. It is not recommended to rotate a head once it's been seated on the tom (the seating is when you initially overstretch the head a bit so that it fits the geometry of the tom), because the geometry of the contact surface of the head and the tom will be affected. The same goes for switching sides.
My advice is to keep your resonnant head where it stands, and get a new batter head: the resonnant head is in place, well seated. It needs changing from time to time, but at a much lower frequency than the batter head. If you switch heads, you'll get to buy 2 new heads fairly soon.
You may want to read the Drum Tuning Bible which gives some very useful advice on drum heads and shells.
I would strongly advise against it. The resonant head is supposed to resonate. If you have beaten your batter head to a point where it should be changed as a batter head, it really means it should be changed. It's beyond the point of optimal resonance and thus using it as a resonant head will not produce a good sound.
Batter and resonant heads don't necessarily need to be the same. In fact, it's fairly common to use a thicker (2-ply) batter head with a thinner (1-ply) resonant head. You can also use the same heads for both, but in that case thinner 1-ply heads are usually preferred.
What really matters is how your heads work together. They don't need to be the same pitch, even though that is the common way. More often than not same tuning, or tuning resonant head slightly higher is what you want, though.
Whatever heads you have, make sure they are in good condition. Heads wear out over time and this is why it's recommended that you always change them before studio. Old, beaten, worn out heads simply do not resonate enough to produce a good sound.