I might get tarred for this, but I've always found LDS missionaries to be really pleasant. I have several returned missionaries as students and colleagues, and they're all pretty personable and good-natured. They're just kids and they spend all day either getting doors slammed on them or being called idiots. So...maybe just be nice to them? For the most part, they want to be on their missions about as much as any of us ever wanted to be in service. Even worse, most of them go to two years with only talking to their families a couple of times. They're lonely, far from home, physically exhausted, and complete outsiders.
So extend some kindness and don't mock them or their beliefs. You can be a lot more effective in planting seeds of doubt through casual conversation than through interrogation and pigeon-holing.
Oh, and as far as caffeine goes: It is not official church doctrine that they can't consume caffeine (I think their own FAQ addresses that, actually), but most Mormons interpret D&C 89's reference to "strong drinks" to refer to caffeine, so they do avoid it. Caffeine in chocolate, medications, and other sources than coffee and tea isn't seen as taboo at all, and many younger or more lax Mormons will have the occasional soda.