Sheldon asks Trevor if he works for the U.S. Government. Trevor says he works for the DMV. The DMV is a state government organization, yet Sheldon doesn't notice or point out the difference.
Sheldon has an eidetic memory...if he had been given the names of the people on the flash cards even once before, he would remember them.
Despite Sheldon being well known for his eidetic memory and remembering very specific details, he had to think because he couldn't remember the celebrity Chloe Kardashian when Penny was quizzing him with flash cards. He then remembers because he had to use a memory trick, which given his character he shouldn't have to do.