You can safely go up to 42 weeks before things start to go down hill. It is very unlikely that you won't go into labour before 42 weeks, but it has happened. A friend had 2 of hers at 42+2.

The placenta can start to deteriorate around 42 weeks, so there'll probably be talk of monitoring/induction before then. But my gp/ob wouldn't consider induction til 10 days past due. Even then it was only discussing it.

If worried you can be monitored every couple days to be on the safe side