The fact is that in 99 per cent of Conveyancing transactions there are no problems on completion. There are a couple of things you can do to help the completion process go more smoothly but you cant eliminate the risk completely as a chain will only complete as fast as the slowest party in the link.
First make sure your Conveyancing lawyer gets all the money they need together the day before; it will be you that has to pay the interest after all so they should not give you any major problems. You should be sent a completion statement a few days before completion.
Second, and most importantly – do not hand over your home keys until your Conveyancer has told you that the matter has completed. Even if you have a great relationship with your purchaser, if they haven't paid for the property then they are not legally entitled to set foot through the door.