Other mistake: After the Doc looks in the book that Breslin told him to, he tells the guards to go get him. He says to go get Breslin from A Block, however the subtitles say E Block. Breslin was moved to E Block and then moved back to A Block after he negotiated with Hobbs. But the Doc says A when the subtitles say E. (01:20:05)
Other mistake: When Ray attempts his first escape, he emerges from the front right side of the fire engine. When he explains how he did it, he appears too far in front of the fire engine to make it look like he was underneath it. (01:07:25 - 02:13:40)
Answer: It proved to the doctor that Ray was who he said he was.