> The first problem is a non-issue. You don't need the voting machine to do the authentication if you let a human control the ballots that get stamped/marked/whatever.

The machine can register what was vote was cast at 13:42. From there, the whole idea of anonymity disapears.

> The second problem also isn't a problem

The impossibility to have the second criterion is a problem because it prevents the first criterion from being verifiable by anyone.