I agree halftail, coyotes get shot on sight, year round here. They are the worst thing to happen to deer, ducks, upland birds, pets, livestock, etc etc etc.
I have shot cripples before, and I have let them slide by.
I think alot of people think that a broken leg or similar injury is always lethal. Sometimes it is, but I think alot of people would be amazed at what animals can live through.
Point: My old man killed a nice buck with his bow a few years ago. As I was skinning it, i felt a lump in his spine just forward of his hips. There was a broadhead lodged in his spine all encrusted with calcium. It had been there at least two, and most likely three or more years. As a skun further I noticed a hunk of scar tissue on his front shoulder, low and behold theres a healed up bullet hole on his front shoulder. Upon further examination we found his front shoulder had been broke, and healed. There was wound evidence on the inside of his chest cavity as well. My dad said this buck was moving as easy as could be and showed no evidence of ever having been wounded.
My girlfriend shot a crippled doe last year, she had a crater of a wound on her right hip. We couldnt tell untill we had her on the ground, again, she was moving just fine. It was infected, and smelled, we ended up discarding her due to the infection factor and not knowing if it had gone systemic, but there was no bone damage, and I maintain she had a very good chance of surviving.
I have called wardens on cripples and vehicle injured deer, all I get is "we'll let nature run its course". (Which is a bunch of BS when dealing with car hits with all four legs broken)
If it was just a single leg injury, that animal has a better than 50/50 chance of making it.
I wouldnt worry about it, if you see the deer again, and notice maybe that its a little more serious of an injury, than Id finish em off.
Boone