Slipped slates rarely cause leaks immediately — there's usually a gap of weeks or months between the slate moving and water making it through to your ceiling. That gap is your opportunity to catch it cheaply.
What to look for
Walk to the opposite side of the street and look up. You're looking for: dark gaps where a slate should be; slates sitting at the wrong angle; slates that have slipped down the roof and lodged against the gutter; or — in winter — anywhere snow has melted off but a single slate or pair of slates still has snow.
When to call
If you can see a gap, call a roofer. Don't wait until water comes through. Slipped slates that fall typically take their neighbours with them, and the cost difference between fixing one slate and fixing five is significant.