Both Taub and House are trying to check if Maggie's daughter can be a bone marrow donor. If they were real doctors they'd know that children never make more than 3 out of 6 match - children only inherit half the chromosomes from their parents. So a 5 out of 6 match "from Cleveland" is by all means a better option.
When Dr. Taub is intubating the patient when her lymph nodes block her airway, he stands behind her and forgets to remove the pillow from under her neck, one needs to extend the neck to intubate. Also he holds the laryngoscope in the wrong way , the blade should face the leg of the patient.
In the beginning of the episode, during the climbing scene, it is show that the rope runs out, thus leading to the fall. This physically impossible while top-roping.