The .22 magnum is one that is sometimes controversial, but much less so than the .17 HMR.
My predator hunting is limited with the .22 mag, so I'm no expert. But, I do have some experiences, though admittedly few. I'm kind-of thinking like Chris Brice does, that we generally don't grab a .22 mag to go predator hunting, but won't pass up a reasonable shot of opportunity either.
I know some guys are limited to rimfires, but that doesn't have to stop them from predator hunting. If a .22 long rifle was all I had or all I could legally hunt with, I would do it, and I would be successful. I would just have to be a little more cautious of taking shots. But then, we should do that anyway, even with centerfires.
I zero my .22 mag at 60 yards to hit center bull. I'm sure the cartridge is capable of over 100 yard kills, but I'm just personally not comfortable taking shots at those distances. Under 100 yards, more like 50-60 yards is where I feel satisfied with mine.
My limited experience with the .22 magnum has accounted for one coyote, one bobcat, one gray fox, and a few groundhogs.
The coyote was head-shot at roughly 75 yards, dropped like a ton of bricks. The bobcat was angling toward me at about the same distance. The bullet hit it in the chest area, and passed through the other side, dropping it on the spot. Both were shot with a 40 gr. Winchester Super-X Hollow Point.
The gray fox was robbing the neighbor of his chickens in broad daylight, and all I had was a 40 gr. FMJ. I shot it broadside. The fox ran a short distance, then walked around a bit, then fell over dead about the time I was preparing to squeeze off another round. I'm guessing distance to be 60-75 yards. It's been many years since, and I don't remember if the bullet exited or not, but I'm thinking it didn't. I do remember skinning it out and sold the pelt for $35, but I don't recall an exit.
Groundhogs are stocky and tough. They can take a lot of punishment and still get into a hole. I've shot them to pieces practically with a 22-250 and had some crawl into the hole. With the .22 mag, I and some friends have taken a few groundhogs. Most didn't make it into the den, but the cartridge doesn't always anchor them on the spot either.
A lot of guys say to not use head shots, I'm sure due to their own experiences. But for me, I have taken several animals over the years with head shots. I don't recall ever losing an animal to a head shot. If I feel I can put the bullet in the right spot, I don't hesitate. I have seen my Dad many times drop large barn-yard hogs with one well placed shot from a .22 long rifle.
The .17 HMR gets beat up pretty bad on these forums sometimes, and rightfully so under certain conditions where people try to use them for something they weren't designed for. But, speaking of head shots, a couple of years ago my son, some friends and I groundhog hunted the entire summer with rimfires only while working on a movie. We consistently dropped groundhogs on the spot with head shots from the .17 HMR, some at distances close to and over 100 yards. We shot a lot of groundhogs, and didn't lose a single one to a head shot with the HMR. We did lose one to a poor placed body shot, however. Just noting what works for me. My advice: If you are comfortable with head shots and know your rifle, go for it, but if not, then maybe don't do it.
Knowing your rifle's accuracy and trajectory means a lot. Practice is everything, and when the time comes to squeeze the trigger, you should reasonably know whether you should take the shot or not.
The .22 magnum has it's role like everything else. you just need to know what it will do and use it within that boundary.