Sheldon has an "eidetic memory"; he would be able to reproduce the missing paper during the train ride.
The guys are traveling on the Amtrak Coast Starlight to San Francisco, which is the correct train for that route. However, the train car shown is not like any train car on the Coast Starlight. Also, they talk about going to the Parlour Car for drinks. The Coast Starlight Parlour Car is only available to sleeping car passengers.
The Pacific Parlour car on the Coast Starlight was restricted to sleeping car passengers only. (It was removed a couple of years ago.) The car the boys ride in is not a passenger seating car on that train, but looks like one of the coach passenger seating areas on the upper level of the Cafe car.
The Coast Starlight does not have a stop in Pasadena. The guys would have had to drive to Union Station in Los Angeles or the Metrolink Station in Van Nuys to board the Coast Starlight.
When Sheldon is on the phone with Penny and hands the phone to Leonard, his phone isn't showing a phone dialing app.
At Sheldon's insistence Raj, Howard, Leonard, and Sheldon purposefully sit on the Pacific Ocean (westward facing) side of a train going north from Pasadena to San Francisco (for the better view). The train departs Pasadena at roughly mid-morning and almost immediately Raj takes the opportunity to grab a "beer" in order to speak with Summer Glau who is seated across the aisle a row closer to the front of the train. While talking with Summer, Raj is quite charming and to impress Summer he gazes out of the eastward (non-Pacific Ocean) facing window to point Venus out in the sky. It has to be at least mid to late morning when Raj notices Venus. Venus would not be visible in the sky at this time of day because it is a "morning star" that can only be viewed from Earth near sunrise or sunset. Raj is depicted as an astrophysicist and wouldn't have mistaken another object for Venus, nor expected to see it at that time of day.
The Coast Starlight does not go to San Francisco. San Francisco passengers would have to leave the train in either San Jose or Oakland and take commuter trains to San Francisco.
The view from the window as the characters are boarding the train is shot at the Burbank (Bob Hope) Airport, several stops from where they live in the series. The train then departs heading southbound, away from San Francisco.
Sheldon planned to leave the Coast Starlight in Oxnard and take a train back to retrieve his flash drive, and then take a taxi to rejoin the Coast Starlight in Santa Barbara. After the northbound Coast Starlight arrives in Oxnard, the next southbound train does not leave for 90 minutes (an hour after the Coast Starlight has left Santa Barbara).
In other episodes Sheldon is extremely excited to be in the presence of recognizable names from the world of science fiction, such as Stan Lee, Wil Wheaton and Brent Spiner. However, in this episode, he is almost entirely indifferent to being in close proximity to Summer Glau, the star of one Sheldon's favorite shows, 'Firefly'. Unlike the other male characters, Sheldon is not in the least intimidated by beautiful women, and yet he still barely even comments on her presence.