Where passengers lose claims by accident
How the three hours are actually counted

The clock that matters runs at your destination, not at the gate you left from. People talk themselves out of valid claims by measuring the wrong end of the journey.
Compensation begins at three hours late. The mistake almost everyone makes is measuring the delay at departure. The Regulation, as the Court of Justice reads it, cares only about when you reached your final destination.
The doors, not the wheels
Arrival is the moment at least one aircraft door opens and passengers are permitted to leave. Not touchdown, not the moment the aircraft reaches the stand. That distinction is worth real money on a flight that lands two hours and fifty minutes late and then waits twenty minutes for a free gate.
Connections are one journey
If you booked a single itinerary, the destination is the last airport on it. A ninety minute delay on the first leg that makes you miss a connection and arrive five hours late is a five hour delay, not a ninety minute one. The distance that sets the amount is measured the same way: a straight line from where you started to where you were going, ignoring the stop in the middle.
Book the legs as separate tickets and this falls apart. Each ticket is then its own contract, and a missed connection is your problem rather than the airline’s.
Take off late, land on time
A flight can leave four hours late, make some of it up in the air, and arrive under the three hour threshold. No compensation is due, however miserable the wait was. You are still owed care while you wait: food, drink, and a hotel if the delay runs overnight.