One local slip
A single slate can often be re-fixed without disturbing a large area.
More than one changes the picture
If slates keep slipping from different parts of the same roof slope, the problem may be with the old nails or fixings rather than with one individual slate.
The replacement has to fit properly
The replacement slate needs to be the right size and thickness so that it sits properly with the surrounding slates. A perfect colour match is less important.