During the 1999 portion of the episode, Leon Stiles drives the stolen car from a location near Trinity site, New Mexico to downtown Los Angeles, CA. After Al catches up and confronts him, Stiles then drives all the way back from where he started. It was mentioned that Al only has 90 minutes to track down Leon and bring him back, and makes it seem like L.A. was 20-30 miles down the road. In reality, the shortest drive would have been over 1,500 miles and a full day driving non-stop.
Previous episodes established that young children can see Sam as he really is, yet Becky specifically says Sam looks like the picture of Stiles.
A highly secure government facility with advanced technology would have easily been able to trap Stiles in the elevator before he could leave the facility.