Dave wrote:

A friend has lent me some DVD's recorded off air
The first time this happened he told me that it had not
been finalized.

That was my first thought.

He took it back and finalized it and it worked fine when
he brought it back for me.

All the D VD's are RW, but he is under the impression that if he
finalizes them he will not be able to re-write them.

Finalising won't prevent erasing them, but will prevent writing anything
else to them *until* they've been erased.