Tire blow outs...
The last tire that blew on me, was in a landing actualy,.excessive nose down, veering to the right...took all opposite control forces to maintain directional control including directional thrust management, with extremely heavy braking. Had I been a little faster on at touchdown, the nose tire would have separated from the nose gear, and what turned out to be simply changing a tire, would have resulted in an incident at the very least. I was in a turboprop...had this been a jet, with less assymetrical thrust to counter the veering, and faster speeds, this would have been an accident, as I wouldn't be able to control the direction and the gear would have impacted, metal to pavement after the tire separated..
I am convinced that a blown tire on take off would create the following scenario
-1 Directional control issues
-2 Vibration (thumping)
-3 Excessive drag / Force impeding acceleration
Obviously if you identify this prior to V1, you stop. If you never identify it it you might not get off the ground at all. Post V1 the issue would be trying to accelerate past v1 to Vr. Same result.
Some of the latest accidents suggest the pilots kept chasing V1 or VR all the way down the runway, when they ran out of runway...some tried to pull the plane off at the end, others didn't...same result.
Base on personal experience I don't think identifying a blown tire is difficult, it's a violent experiece...just like in a car...the issue is trying to figure out with your new speed paradigm if you can make it to take off, or if you should stop...all your pre briefed V speeds just went out the door...