Question: When the fake Professor Moody is in his office with Harry, revealing everything he did, Dumbledore charges into the room with Professors McGonagall and Snape. All three of them are prepared to attack when they enter. How did they figure out that something was wrong?
Answer: If we look closely at the scene where fake Moody takes Harry away, Fred and George are looking at them. It is quite likely that they informed Dumbledore who instantly became suspicious.
Answer: Adding to the other point, you wouldn't take a child who mentioned Voldemort's return away without the inquiry so Dumbledore must have realised that Moody was trying to get Harry away from the situation.
Question: Why did Hermione take off one of her shoes after the Yule ball?
Answer: She had been dancing for a long time and her foot hurt, so she took her shoe off to rub her foot.
Answer: Because she had been standing on them for hours and her foot hurt.
Answer: Her foot was hurting. She had her shoes on for a long time. Or maybe Krum stepped on her toes a lot and it hurt.
Answer: It is also possible that her foot cramped up.
Answer: Because she was angry and her leg hurt.
Answer: When it was noticed that Harry was missing during the commotion surrounding Cedric's death, someone in the crowd saw Moody leading Harry away and tipped off Dumbledore. Dumbledore knew that the real Moody never would have taken Harry away like that without telling anyone. Also, Snape is a legilimens (able to read minds) and would be able to "hear" Harry and Moody's thoughts.
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