When Claptrap asks what happened to Sam's voice, Sam mentions that his old voice sounded "Goofy". His original voice actor from Sam & Max Hit the Road was Bill Farmer, the long time voice actor for Goofy.
Brock mentions that he was included as a unlockable character in a (fictional) Mortal Kombat knock-off without his permission. Claptrap says that that he had a "death smooch" fatality in that game (Sonya, Kitana and Tanya all had kissing fatalities at one point) and, parodying the eventual transformation of Midway Games Chicago into Netherrealm Studios, Brock adds that "the company went bankrupt... with extreme prejudice."
If you listen closely during the introduction, you can hear the sounds of someone playing Johann Sebastian Joust from Sportsfriends right before Brock knocks the bandit out of the room. Evidently, the way to achieve surefire victory at Joust is by stabbing your opponent.
Change to the Sam & Max inventory for the first time, and Sam will exclaim: "Great gallifrey, Max! It looks like our past is spilling all over the Inventory!"
Claptrap's bounty item is his Spike TV VGA 2012 Character of the Year trophy. The first time it's pulled out, GLaDOS claims that it looks familiar, which is perhaps because she also won a Spike TV award for Ellen McLain's portrayal of her in 2011.
Brock mentions that when he heard he would be playing poker with "Ash Williams", he was expecting a girl. Ash says he's been getting a lot of that lately for some reason.
There are smooth jazz versions of the Venture Bros. theme song, "No Vacancy" (it's a little difficult to recognize but it's there) and "Short Change Hero" by The Heavy- the opening song for Borderlands 2.
In another conversation, Brock asks Sam if he ever considered fighting with a blade. Sam mentions he did, with an axe, but that lead to confusion when people kept calling him "Sam Axe". Ash thinks that name is dumb.
Ash's hand being possessed by ad execs and spelling out "DRINK MORE BANANG" in Morse Code may be a modified reference to A Christmas Story.
It's also not only a Call Back to Sam & Max, but also to the previous installment of Poker Night in which Strong Bad claims to like banangs.
Banang makes appearances in almost all of Telltale's games, including the Sam and Max games and the Walking Dead
If he wins a few times in a row, Claptrap asks if there's a glitch in the The Matrix, because he's getting deja vu.
When commenting that his chainsaw is leaking, Sam sarcastically asks if Ash is preparing for an Attack of the Triffids. (Attack of the Triffids is a notoriously bad horror movie featuring what is widely considered the least threatening movie monsters in film history)
Likewise, in the Sam & Max 25th Anniversary room EVERYONE (even GLaDOS) will serenade the duo with a song about their adventure in Hit the Road.
When Claptrap comments that Sam and Max's first official appearance was 26 years ago, Max shouts "NERRRRRRD!" while Sam explains that they always skip over 2004 when counting. A running gag in the Telltale Sam and Max game is that everyone tries to forget that year and the "particularly gruesome" case that took place that year (i.e. the same year the sequel to Hit the Road was unexpectedly cancelled by Lucasarts).
If a game is going relatively quickly, Brock might say he might be able to get back in time for Downton.