What Should and Should Not be Done

Shop around for the best mortgage deal and advice you can get: check how each lender handles interest rate changes and what the policy is of individual lenders.
Compare interest rates between lenders
Try to negotiate the lowest interest rate. Start with a low rate from one, and then haggle with the others for a lower rate. You might be lucky if they want the business.
Also shop around for your home insurance and life insurance. Negotiate discounts for taking them both with the same insurer, and also with your lender for a better deal if you also give them your insurance business.
Make sure your broker is representing a fair number of lenders. The more the better for you.
Keep a file containing all correspondence in a safe place.

Do not accept the first offer you are made. You might get a better deal elsewhere and you can always accept the original offer later.
Mortgage Protection Policies can be expensive - shop around. You are not obliged to purchase that offered by your choice of lender.
Free offers to first-time buyers can end up not so free. Special offers can eventually cost in the form of progressively increasing interest rates.
Never miss a payment. Not only can you lose your home if you don't pay your mortgage, but your rating with other lenders will be dramatically reduced: your mortgage should always be considered your 'first-to-pay' expense.
Mortgage lenders can be understanding if you are honest with them. If you are experiencing financial difficulties then tell them. They might be able to help, but not if you simply don't pay.