They can use a 'damage your opponent action' with a successful grapple check but that would just do non-lethal damage equal to ... hmm well I don't see what it is equal to in the SRD but I'm pretty sure its their size modifier. D3 for medium so what's that? d4 for large, d6 for huge, d8 for gargantuan and finally 2d6 for colossal. To an 18th level character this is just chump change they could take this damage all day. Though the dragon can do this move once per 6 points of its BAB so adding it all up might be notable.
A better option, I suspect, is for the dragon to use its natural weapons in the grapple. It gets a -4 to hit doing that (no grapple check required) but the damage is lethal and it sure has a lot of good natural weapons.
I believe Ninjack was referring to the fact that a dragon with the Snatch feat essentially gains Improved Grab with its bite and claw attacks, which allows it automatically inflict damage on the grappled target as if it struck with the natural weapon used for the grapple on any round in which the dragon maintains its hold. Considering this is essentially automatic damage, and the dragon can still either take a full attack with all its other natural weapons or use its breath weapon with no save allowed (if grappling with the bite), that amounts to significant damage. The only problem is that it can leave the dragon vulnerable to other attackers, but as was stated earlier, the -20 grapple penalty to avoid being considered grappled probably doesn't hurt a dragon too much.
As for giving the dragon Combat Reflexes, it's actually not too impressive. Since it only allows a number of extra attacks equal to your dex bonus, and dragons rarely have a Dex score above 10 without being given the Elite ability adjustments, that translates to 0 extra AoO's. The only benefit it would get is being able to make its one AoO while flat-footed.