A horse is deemed unlevel when its hind legs are clearly not equally active. That usually gets detected in extended trot or half-pass when horse drags its feet, and then it's up to the president of the jury to ring the bell and stop the test. It's a sign of lameness (most commonly momentary lameness).
As for the blood rule, if a spot of blood is detected on horse during or after the test, then the rider receives automatic elimination. Most of the time it happens when a horse bits its tongue, which is bad luck more than anything else. It only gets suspicious when it repeatedly happens to same rider...
Three eliminations in one competition is very unusual though. I can't remember any competition that had more than one elimination. Therefore I'm assuming that the American judge was perhaps overly strict on levelness. I could almost guess that Beca would be the third eliminated rider. His horse has a really weak extended trot, which could make one question its soundness. But then again, I don't think he ever got eliminated for it, even if he usually receives very low marks.