H.R. mentions having Star Trek: Voyager on his Earth, to which Cisco claims to hate spin-offs. This is likely a tongue-in-cheek joke, considering the fact that The Flash is a spinoff of Arrow.
According to Barry's driver's license, it says that he renewed it on March 10, 2014. However, Barry was in a coma from the time of December 11, 2013 to September 2014, meaning he couldn't have renewed it during this time, assuming that it has to be renewed in person (unless a military member or dependent) like in real-life Missouri that Central City is placed in.
After losing his memories, Barry asks to be called "Bart", a reference to Bart Allen, who is Barry and Iris' grandson in the comics. Ironically in the Arrow episode "The Brave and the Bold" Quentin Lance mistakenly calls him Bart which also references his future grandson in the comics.
Barry is revealed to have been a huge fan of anime in high school, with Iris mentioning that Dragon Ball Z was one of his favorites.
Coincidentally, this episode aired on the Japanese-recognized holiday "Goku Day".
Rather than "the Flash", Barry suggests that they call him "the Streak", a name which was first used to identify The Flash in the first season of the show and also, a moniker used by Clark Kent on Smallville.
Tracy states they require 38.6 Terajoules (38,600,000,000,000) of energy to trap Savitar, and Cicso claims this is more than the energy of the Sun; this is vastly inaccurate, as the Sun releases 384.6 yottajoules (384,600,000,000,000,000,000,000,000) of energy every second.
When Savitar says that Barry killing himself won't stop him, he cites Eddie Thawne killing himself and Eobard Thawne's continued existence as a time remnant as evidence (Although Thawne's remnant eventually ended up being erased from existence on DC's Legends of Tomorrow in "Aruba").
As Savitar's armor begins to attack Barry, Barry's mask is removed. However, shortly prior to the armor stepping on Barry, his mask is seen worn on his face.
Even after examining his driver's license, Barry doesn't believe Team Flash when they tell him that his name is Barry, in spite of his signature clearly reading "Barry Allen." However, it is possible that Barry didn't see his signature.
He instantly recognizes himself without being surprised at all when Iris shows him a photo of him and her in a relationship on her phone.