First-time home buyers should avoid several common mistakes after mortgage pre-approval to ensure a smooth closing process. Key actions to avoid include changing jobs, purchasing a new car, making late payments, and opening new bank accounts. It's also crucial not to spend down payment funds, offer more than the appraised value for a home, close debt accounts, co-sign new loans, skip home inspections, or ignore lender requests. Maintaining financial stability and consistency is essential until the loan is finalized.