What's the capital of Texas?
Lea Thompson wakes up Powers Boothe and tests his loyalties with the question, "What's the capital of Texas?" to which he responds, "Austin." She corrects him that it's Houston, but seems confident that he is truly an American.
A minute later when he's giving them the run-down of how the invasion occurs, he mentions that his family was stuck behind enemy lines in Texas, which we are led to assume is his home state.
So, how did he not know the capital city of his home state? I know he said he was tired when he was woken up by Thompson's character, but I don't feel that's the kind of thing you forget just because you're groggy.