Towerdog,
Some years ago I recall a QF 767 blew a number of tyres and taxied to the gate to then be followed by an emergency evac (at the gate with slides). Does anyone remember how many blew?
Quite a number of years earlier I recall a 727 doing crew training touch and go's out of MEL. They blew 2 tyres on the same gear, punched holes in the fuel cell, flaps, spoilers and took out most of the brake lines (the hydraulics were saved by the brake de-boosters). The only reason the crew aborted the take-off was because they couldn't read the airspeed correctly due to the intense vibration as they started to accelerate.
This aircraft taxied to the gate; the brakes, wheels and axle sort of all became one when it stopped.
As stated by a number of posters you probably wouldn't notice the change in angular reference; but there would be other signs.