You know, they’re all hanging upside down and stuff - do they crap while they’re hanging there, or do they hold on until they’re flying around so the poop falls down, and not running down their fur? Are there prehensile rectums involved?
I’ve not witnessed it in action, so to speak, but based on the mess by my front door where a bat lived until about two weeks ago, they poop right where they hang. Not sure if they’re able to aim it away from themselves, or if they do it right as they take off.
Many birds will defecate on take off (sort of lightening the load). Also, I believe in this context the phrase “bat shit” is appropriate. 
This question brought the house down when asked by a 5 year old at carlsbad caverns. “If bats hang upside down, how do they go guano?”
The answer:
In addition to thier rear feet, bats have a coupel of hook-like fingers located near mid wing. (like if we had claws on our elbows) They can hang by these, let go with thier feet, and rotate to a vent downward position for defication.
Well, isn’t that an elegant solution - just do a few gymnastic manoeuvers, and no mess crapping.
(We discussed the jettisoning ballast that birds do - the phrase “Jet-assisted take-off” came up. :D)
Reminds me of that classic joke:
A bear asks a bat if it has a problem with poo sticking to its fur.
The bat says, “Why goodness no, Mr. Bear. For you see, I simply rotate myself…”
The bear immediately picks up and wipes his ass with the bat before it can finish.
Thanks for injecting that intangible air of class, Controvert.
Semi-Hijack
Male bats will urinate while hanging upside down. They’ve evolved so that the stream comes out at sufficient pressure, and is cut off so cleanly, they don’t get a drop on themselves. A tiny penis emerges from the sheath, hangs just two over the bat’s head, and not a drop gets on the bat. It’s awe inspiring.
I was not fortunate enough to observe any of the specimens defecate. While they certainly did have thumbs (the structures Kevbo mentions are homologous to thumbs. The points along the bottom edge of the wings are the tips of the other fingers. Bats are members of the order Chiroptera* meaning “hand wing”), and could have defecated while flying, I wonder whether they’d evolved rectums which could be cleanly used while upside down.
The majority of bats also engage in grooming behavior. If one has gotten guano in its fur, its pals will lick it clean.
Re Lightening The Load
Vampire bats (of which they are only two species, both with a distribution centered in Central America) have a diet that is mostly water. They’ve evolved kidneys so fast and efficient, that they begin urinating almost as instantly after beginning to feed. When they take off about 60 seconds later, they’ve already filtered all the water from the blood they’ve ingested, and excreted it in their urine.
- Technically divided into two suborders, Megachiroptera (flying foxes and the other huge bats) and Microchiroptera (everybody else).
As all rodents are members of the order Rodentia, we can see that bats are not rodents, despite names like fliedermaus (flying mouse) etc.