Concave (magnifying ) mirror wouldn't be much use IMHO. I can see that a convex mirror might be a good idea. A concave mirror is fine for shaving when you want to see fine detail on your face. But as you know, when you move back from it, the image becomes very distorted and then actually inverts. This wouldn't be useful for guttering inspection.
(If you don't shave, or use your mirror for putting on make up, the same is true.)
My reasons for saying that are that you don't really need to be seeing much detail. You want to know that there is a certain depth of muck in a gutter, you don't need to do a chemical or colormetrical analysis of the soil type.
A bit of physics here: the image that you see in a plane (flat) mirror depends on two things: the size of the mirror and the distance you are away from it. They both change at the same rate when you move towards or away from a mirror. Therefore moving the mirror back and forth doesn't alter how much you can see. (I know that this is non-intuitive, but it's true.)
You can test this the next time you go into a clothes shop with a full-length mirror. No matter where you stand, you can always see the same amount. So stand closer and you'll see better! Incidentally, a full-length mirror for you is one which is exactly half as tall as you are. Anything more than this is more than full length.
With a convex mirror, you'd see more as you moved the mirror back, but it would appear smaller.
I agree with Kev that it might be worth experimenting with at some time. If I do, I'll report back.