I just was wondering what would happen if all but one of the validators see +2/3 precommits in a round and thus commit but one validator does only see, let's say, 1/2 of the precommits (because of lost messages) and thus goes into the next round.
How is this problem handled by Tendermint?
Validators who committed a block X will send the last commit to that validator. When the last commit is received, the validator will progress to the next height X.
If it doesn't receive anything, other nodes will still try to send commits so the validator can catch up.