Some things to check or ask in general.
How do they handle vents? o Plain air vents
---- some just cement them all up (wrongly)
---- some insert hollow plugs or sleeve, for free or at a cost
---- min house ventilation for gas fires 500mm in insulation
---- eg, small CSA shower cables in cavity are at risk
Do you have any cavity damp problems? o Usually very obvious re darker coloured bricks
---- white staining on walls from salts etc
---- down a wall or visible at damp course o Typical cause is a cistern filling to near the overflow
---- wind gusts into overflow, wave washes water out
---- overflow pipe tilt is insufficient, water wets wall
Verify your cavity is dry before you stuff it :-) Least likely is penetrating damp unless in a moat.
Do you like your wall colour? o When they drill to push insulation in, catch the dust
---- when they fill the holes in, add dust in to match o Avoids cement or clear-but-not-invisible silicone
Do you have outside chimney(s)? o Verify they are aware of their location if not obvious o Not a good day if they drill through a refractory lined flu
If you plan on bashing the living daylights out of a cavity wall, it will make insulation settle & may need a top-up. Same goes for drilling 6" extractor vents and such like, indeed the former could almost be fun with polybead...
The difference roof/wall insulation make is very very big. Roof makes a big difference, wall as big a difference again.