Accidents have occurred to aeroplanes taxiing when one brake has failed, or a nose wheel steering system has jammed. Collisions have occurred when the pilot has misjudged his clearance from an obstruction such as another aircraft, so it is logical that we should allow as much space as possible between ourselves and collision hazards while taxiing.
We should also be aware of any abnormalities, such as one brake pedal developing greater movement than the other. However, other abnormalities may occur, and if we can detect these and take appropriate action early enough we may be able to prevent an accident. If for example we find that we need to apply steering or braking continually in one direction without an obvious reason such as a crosswind or sloping taxiway, we should suspect a binding brake or a problem with the steering system, either of which may cause serious problems on take-off.
If we require a higher throttle setting than usual to maintain our normal taxi speed, it may be that both the brakes are binding, or it may be that we have forgotten to remove the parking brake. Taxiing the aircraft with brakes applied is likely to cause the brakes to overheat, damaging them and perhaps starting a fire, which reportedly happened to a Cessna 172 recently.
We should all know what actions we should take if the brakes do catch fire. However, if we know our aircraft and can detect problems before they become serious, we should hopefully never have to take them.