Ask the adjuster to admit that their insured (the other party) was at fault.
The adjuster will always want to ask plenty of questions about where you were going, where you had been, how fast you were traveling, where you were looking, etc. Each question asked by the adjuster is designed to yield information that will potentially reduce how much money they will pay you. Turn the tables on them. When the other party is at fault, ask questions about facts that any honest person should freely admit. For example, "Do you agree that your driver ran the red light?" or "Isn't it true that your driver was speeding?" Listen to their answer and repeat the question. An honest adjuster will admit the truth - if they won't - be on your guard.
Ask the adjuster for a copy of their insured's statement (the statement of the other party).
Adjusters will always want to get a recorded statement from you as early as possible, but they will be running the interview so the outcome is seldom in doubt - they will get something from you that they can use to reduce their pay out on the case. Before you agree to give your statement, ask them for a copy of their client's (usually referred to as their "insured") statement in exchange. They will probably say that they can't do it, that it's against policy or make up some other excuse. If this is about getting the facts and the truth, why not? If you give them a statement (which is an advantage to them), what are you getting in exchange?
Ask the insurance adjuster how much insurance is available.
Knowing how much insurance is available helps settle lawsuits and claims. If the insurance adjuster wants information from you, this is an easy thing they can provide you in return. Unfortunately you will hear excuses more often than not about why they couldn't possibly tell you what the coverage is (even though you can go online and for a few dollars find out). If all the adjuster wants is a one way street - you have to ask whether there is any chance they will be fair when the talk turns to money.