Week 4 of your escrow, and any other weeks past this point are about finishing up business. With all contingencies removed, both buyer and seller can address the last issues of moving their respective households.
Approximately 3-7 days prior to the official close date, the buyer/buyer's agent will likely do a 'walk-through.' They come visit the property one last time to check on the following:
1) Whether the home is in the same condition as it was when the offer was signed
2) The repairs that the seller agreed to make
There certainly have been fall outs on both fronts in my experience. If the seller removes anything that was agreed upon, changes out appliances, chandeliers, or wall coverings - these things will all wreak havoc at this late stage.
The buyer side also will want to be comfortable the seller completed the repairs requested. It is a good practice to offer invoices/receipts from the vendors that performed any repair work. These go a long way towards reassuring the buyer that repairs were performed correctly.
Once the walk-through occurs and is signed off on, the buyer side will be in close contact with the lender. The buyers will also be signing loan documents during the last week of escrow. Any delay in loan documents will mean a delay in your close date. In my experience, there are delays 40-50% of the time, so sellers, be prepared.
As a seller, your job is to cooperate with any paperwork that needs signing either by escrow or the buyer side. You may want to coordinate utility transfers between seller and buyer, and make sure that all keys (mailbox, complex, building) are ready to give the new buyer.
If all has gone relatively smoothly, you can look forward to a smooth close of escrow. Congratulations!