First question, you are correct. Since the two hot legs are 180 degrees out of phase, if you are drawing 20 amps on each, they balance and the power essentially feeds back and forth through both hot legs. The neutral has zero current. The worst case for the neutral is if you have 20 amps on one circuit and zero on the other, then you get 20 amps back through the neutral. Think about it - if you are running a 220 volt load on the two hots, you can disconnect the neutral and it would still run fine. (Don't try this at home, kids.)
The downside of the common neutral circuit is that if you need GFCI protection, the only way to get it is to use a 2 pole (ganged) GFCI breaker which is very expensive.
I'm not sure what the other poster actually meant by "drop a neutral". If the neutral becomes disconnected, neither of the 110 circuits will work at all. (A 220 load could be powered, but only if you have a socket wired to both hot leads.) If you short one of the hot leads to the neutral, you would theoretically have 220 across the 110 socket, but you would also pop the breaker, so I'm not sure why this is concern. I guess if you disconnect the neutral at one place and short it at another, you'd get 220 on a 110 socket, but that's pretty farfetched.
The only safety concerns I've heard about with this arrangement is that if you have individual breakers you could trip one breaker and still have power on one side of the circuit in the box and also the concern that if you hook both hot legs to the same phase, you can overpower the neutral.