For the first one, I see the value in going to a centralized place that has taken measures to make sure there is no coercing involved. Someone with a gun could indeed come to your home, and make you vote for a certain candidate. I don't have a good answer for this, but I do feel that it would be a difficult strategy to pull off, as citizens can vote at any time, from any place.
For your second point, this is indeed the hard part. It can be rephrased as: how can you be sure no one was given 2 coins? I also don't have an answer here that doesn't make you associate an SSN or another unique identifier with a wallet address, which would ruin the anonymity feature. Maybe someone else reading has some good ideas to add?