I pay a lot of attention to brakes, wheels, and tires after the high speed taxi check. In particular, I like to have the maintenance staff double-check torque on wheels, tire pressures, and have a look at the brakes using an optical thermometer to ensure that all the pucks are operating as they should.
I also like to taxi over a series of objects such as 2 by 4 boards or perhaps sets of chocks that are used for very small aircraft (the 1,500 lb two seat types) just to see what rattles loose in the aircraft - to find out if anyone has left a tool behind, or failed to properly secure a roof panel, etc.
I'm doing first flights of Twin Otters, not Space Shuttles, but still...
