When Lily visits Marshall in St. Cloud Minnesota he asks his mom if she bought AA batteries because he is on a "sick Dr. Mario Run". He is playing this on an original game boy and switching out the batteries would automatically end his game by turning off the game boy.
When Marshall shows up while Lily is watching Predator (1987), we can hear Arnold Schwarzenegger saying "Come on, come on. Kill me! I'm here... Kill Me!" Then, a few seconds later, we hear machine gun fire. There is no machine gun fire in the movie "Predator" after Schwarzenegger says those lines. These lines are right after he and the Predator physically fight and Schwarzenegger is tempting the Predator into his trap.
When playing the Nintendo Marshall mentions he has Super Mario Kart, a Game for the SNES console, not the 8-bit NES. Later in the episode Marshall and Ted are playing with controllers for the NES Console.
At the end of the episode when Marshall surprises Lily back at the apartment, he comes from the left, which is their kitchen, and Lily is sitting closer to the door, meaning somehow he got in without her realizing it and circled back around.