Which sentence has a word choice error?

The First Lady preceded the president into the Oval Office

The First Lady proceeded the president into the Oval Office

The sentence that has a word choice error is the second one - The First Lady proceeded the president into the Oval Office.

To proceed means to continue - you proceed doing something, or something proceeds on its own, but you cannot proceed a person - the verb is not transitive and thus doesn't require an object.

The first sentence is completely correct - to precede means to walk in front of someone, to be the first one there.