Arin calls an enemy a "Boomer Man". The enemy's actual name? Boomernote Although there is a Broken Base as to whether the enemy in Super Star is actually Boomer, or simply a Poppy Bros. holding a boomerang.
During their Sonic '06 playthrough, Arin made fun of Silver and Blaze's interaction by calling Silver, as Blaze, "so naive". Turns out, in Blaze's next line of dialogue in the game, she calls Silver "so naive."
In an early Castlevania: Dracula X episode, Danny jokes about the terrible posture of some skeleton enemies, comparing them to apes. In fact, their English name is "skeleton ape", and a couple boards later one of them throws a barrel at Richter.
Ascended Fanon: A few of the specials came from common requests and ideas that circulated the Game Grumps subreddit.
A redditor originally wrote what eventually became the Jingle Grumps jingle.
Fans had been demanding a valentines special where Suzy and Arin play through the Lion King on SNES together, since Arin once mentioned it was Suzy's favorite game. Lo and behold, on valentines day 2014, they did a special which was just that, and acknowledged the fandom demand for it.
Fans also had the idea for Ross and wife 'Commander' Holly Conrad to do a valentines special, with Danny and Barry doing a 'bachelor pad'-style episode, knowing they were both single. While Ross and Holly ended up doing a valentines show for FriendZone on Polaris, Danny and Barry indeed did a Steam Train special called 'Singles Train'.
Attention Deficit Creator Disorder: A week into production, they already had five separate games going on at once. Every other episode usually has Jon saying 'We should play...' to Arin.
Beam Me Up, Scotty!: They somehow manage to pull this off on themselves, where they quote the Pause Balls meme as Freeze Balls in early Goof Troop episodes.
Colbert Bump: For Goof Troop. Just type "Goof Troop" into Google and see what the top search is. Additionally, most Goof Troop videos on Youtube have many people making references to the Game Grumps let's play in the comment section.
Generally, anything they mention that you can find online will have a string of comments mentioning how Game Grumps alerted them to it. Ex: This link
Heck, Jon himself can fall under this. While he did have his own following prior, Ego has a significantly larger following, many of them discovering Jon through Game Grumps.
Continue is mentioned several times by Jon, perhaps in an attempt to invoke this trope, considering how he did this sort of thing in his own channel once or twice.
Ninja Sex Party is experiencing a minor boost in popularity thanks to Danny's inclusion on the show (as well as co-hosting Steam Train).
Acknowledged in part 14 of their The Legend of Zelda: The Wind Waker HD, after finishing a quick singalong of "Let Her Cry" and "Hold My Hand" (which leads to them agreeing that they both sound the same).
An old website named Game Grump exists, though they've been inactive for more than a year now. The website is now a parked domain.
Ron Gilbert uses "Grumpy Gamer" for his website name and online handles.
Promoted Fanboy: Flannelson, a popular fan animator, has some of his fan animations uploaded to the main Game Grumps channel.
More recently, Esquirebob, another fan animator, had his Sad Hoshi animation uploaded to the main channel.
Rule34 — Creator Reactions: Jon and Arin are well aware of the One True Bromance nature of their partnership, and have no compunctions about lampshading it.
After they discovered a Rule 34 pic of themselves, they went on to tweet about it, and mention it in at least two different episodes. Egoraptor signs off from Sonic '06 by pretending to make sweet love off-camera (as a "gift" to the viewers).
Polygrumps is followed up on in FireRed part 28, where it turns out Arin is also completely fine with it (and both loves seeing pictures with him with other men and with him and Suzy). In fact, the only person mentioned to be even slightly uncomfortable with Rule34 is Danny, who goes back and forth on the matter before deciding to accept it because it makes the fans happy.