IMHO, it had potential. The problem I see is that it was more complicated than its competitors and thus, at the least, more expensive. I somehow doubt it had many reliability problems, but I can't rule out the possibility, especially with maritime use. I would like to know more about how the charges were ignited. I've seen a very early flintlock revolver, and that was its downfall, because sparks could leap to the other pans and cause a multiple discharge. Maybe Puckle's design averted that.
Another point I just realised is that of, how much more effective would the Puckle have been than the guns already in service. This question comes up because I just (and I mean just
now) learned about breach-loading swivel guns, that allowed several charges to be loaded and ready, thus allowing for firing nearly as fast as the Puckle with less complexity.
Picture at the end.