There has been a delay in the date escrow will close on the house we are selling. The buyers want to move in before the new escrow closing date. Is this a problem if they agree to pay rent?

It could be. Once the buyer has possession, if he decides to back out of the deal, you might have to go through an eviction process which can be costly and time consuming.

If you still want to let the buyer move in, you need to amend the purchase agreement by adding rental terms. Consult an attorney to draft the agreement so you can be sure it is adequate. These provisions should cover how much rent will be and when it is due. Also make sure the buyers do their walk through inspection prior to moving in. That way there won't be any surprise problems at actual closing time.

Upon moving in, the utilities should be put into the buyer's name. Make sure the buyer obtains adequate property insurance. The seller should require that the buyer put a substantial deposit in escrow and sign a liquidated damages agreement. The deposit can be applied towards the down payment if and when the sale closes on time. If the closing is delayed or the buyer backs out, the deposit will be forfeited as liquidated damages. Your agreement should stipulate that the buyer will receive only a portion of his deposit back if he vacates the property.