The so-called "submarine controversy" from Raiders of the Lost Ark (1981) refers to the scene where Indiana Jones grabs hold to the outside of a Nazi submarine and rides it all the way to their hidden island base. The "controversy" is how Indy knew the sub wouldn't submerge and likely cause him to drown. In novelizations and comic adaptations of the film, The submarine does submerge, but Indy lashes himself to the periscope, which remains above water.
Because of her broken leg Kaley Cuoco is shown working as The Cheesecake Factory's bartender again, instead of her normal job as a waitress. Also, a body double is used when Penny storms off near the end of the show.
Penny tells Leonard she can't believe he's never read Eat, Pray, Love by Elizabeth Gilbert. Raj says the book changed his life and later tries to tell the guys about it. Eventually, Leonard can be seen reading it while the guys are waiting in line to get into the movie theater.
The website from which Amy was getting her slumber party activity ideas was in fact Wikipedia. On the page for "sleepover" (redirects from slumber party) lists activities such as Truth or Dare and even "harmless experimentation with lesbianism" and eating raw cookie dough.
While watching "Indiana Jones" Penny comments on the hat which Sheldon attributes to the creative genius of the costumer on the film. In reality Harrison Ford was unhappy with every incarnation of the hats made specifically for him and eventually took it upon himself to purchase an "off the rack" hat from James Lock & Co in St James' Street, London which was fitted for him by shop staff. His conformitor template is still in the store records although it is no longer on display.
The trivia item below may give away important plot points.
The guys actually did make it to the movie on time, yet were still denied entry. While Sheldon, Leonard, Howard, and Raj are in line, Will Wheaton shows up with 3 of his friends. When Sheldon and the others get to the front of the line, the petty functionary with a clipboard tells them the theater is full up. Will Wheaton's group and Sheldon's group each had 4 people, meaning if Wheaton hadn't shown up, the guys would've been the last ones into the movie.