What constitutes a valid alibi? Suppose that Amber says she was with Dan in his apartment when the shots were fired. This indeed gives Dan an alibi (except in level 4). But does it give Amber an alibi? Not yet! You must also ask Dan to make sure that their stories colaborate before you can rule out Amber. The program keeps track of what questions you ask, and will not let you make an arrest until you asked all of these follow up questions.
Finding an alibi is important even if the murderer lies. If you find two statements that don't agree with each other, you will need an alibi for one to prove that the other is the murderer. Suppose Amber claimed to be home alone, while Dan said Amber never answered her phone. Is Amber lying? Maybe, but first you need an alibi for Dan to make sure that Dan is not the one who is lying.
If you think one of the suspects is the murderer, you are much better off asking him questions about other people than asking others about him. Asking the murderer more questions will increase his chances of lying. However, if you ask the murderer directly where he was on the night of the murder, you might make him angry. You don't want to make him angry. (However, if you know that someone isn't the murderer, then it is a good idea to ask them about themselves. They might reveil an important clue.)
Don't be afraid to ask the same person the same question. The person may elaborate the second time the question is asked. This is particularly important on levels 3 and 4, where even the smallest of clues is the key to solving the case.
What constitutes a valid alibi in levels 1 and 2 may not count as an airtight alibi in the higher levels. This is because the murderer can get pretty sneaky in levels 3 and 4. For example, he could call someone from his cell phone, and make that person think he was calling from his apartment. Or he might use the call forwarding feature on his apartment phone. (I don't want to give anyone any ideas.)