Audio problem: When Bond arrives at the King Industries place where he meets Elektra King, watch the man he talks to when he gets out of his car. It is painfully obvious that the man's mouth is not in sync with what he is saying. Even worse, the voice is not even his. It is slightly higher-pitched than the man's real voice when he finally talks right.
Audio problem: In the scene where Reynard and his men are stealing the warhead, Bond jumps and dives through some blast doors as they are closing. While flying though the air, it is seen that he fires a shot. However, you never hear the blast. The flash of the barrel is easily seen, and it is obvious that he is not using a silencer from previous moments of that scene. He shoots, but you don't hear it.
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Audio problem: In the village in Azerbaijan, Bond tells Elektra she might be in danger and she laughs, telling him "I have something I want to show you" as she walks away in a long-shot. It's obvious this line was dubbed in during post-production - there's a very sudden, very noticeable drop in background noise and her mouth (although it's hard to tell from a distance) doesn't seem to move with the words.