That's not about the executioners (in most cases, it's not their fault that something doesn't work), but about the method that has painful failure modes. The point is to chose one that couldn't screw up (for whatever reason), or that is very hard to screw up. Criminals have all sort of problems with bodies, starting from obesity (excessive body mass can really mess with lethal injection), drug abuse, various medical conditions and so on. You need to really know a lot about the guy in order to properly conduct the execution with one of the more elaborate methods. By contrast, hanging requires only to know a person's weight (by far the easiest parameter to measure) and decapitation or firing squad don't require even that. The less variables, the less failure modes and, consequently, less chance for failure (in most cases, that is). That's why I advocate simple, proven methods and not fooling around with needlessly elaborate (and painful) schemes.
Also, I just thought that a sort of mechanized, high-caliber "firing squad" could also be a good method, though it'd probably run into same issues as decapitation. If you put the guns on a stand (as human executioner can miss), make them of high enough caliber (say, 10mm Barret) and aim them at the head or heart with computer, the guy executed shouldn't feel a thing, either. Firing squad is a legal (pretty good in itself, if seldom used) option in US, though I don't think they'd approve that kind of modification. I recall hearing about a guy who actually explicitly chose it over lethal injection, so there might be some merit in this reasoning (it might've been to prove a political point, though, I don't remember).