Checking their work is always a good idea. That said, I was unfortunate enough to have two broken screens in the space of 10 months (heavy stone damage on the motorway), but I wasn't around to check it while they worked. Autoglass did both, and everything worked just fine. No trims hanging off or broken bits - to be honest, you'd never know they'd been working on it if it wasn't for the sudden absence of a big crack.
Important - don't drive the car for a few hours after having it done. The glue needs to set, and as mentioned above, the screen forms part of the structure of the car. You don't want it warping slightly and then the glue later setting hard in what is slightly the wrong place, that can lead to stress cracks later on.