Sheldon abruptly leaves his office without his laptop and gets into the cab with nothing but what is in his pockets. Through the flashback, it is shown that he stopped by his apartment to video call Dr. Hawking for permission, before going to the airport. He is talking to Hawking on the laptop that he left in his office. It also creates the continuity issue that he would have packed a bag if he stopped by his apartment and shows up in New Jersey with nothing but what is in his pockets.
Howard puts his plate back on the table twice when he and Bernadette are having dinner with Leonard and Penny talking about babies.