One very important thing to look out for is when the other party won't give in on something little, inexpensive, and relatively unimportant to them. One example is the credit you receive. If the negotiation is unpleasant, the job will be, too Personalities emerge during a negotiation. Someone can be a hard negotiator, but still be pleasant about it. If they're not pleasant now, they won't be pleasant when you're working with them either.
Life is too short for that.
Once you've agreed to something, you've agreed. Trying to renegotiate something you've already negotiated is like breaking an agreement. It's a sign of bad faith. If someone tries this on you, make your refusal clear, and be warned of future problems. Last-minute additions can make it seem as if someone is trying to slip something in, and they are rarely appreciated and can jeopardize the entire deal.