These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Foe Yay Shipping: Fangirls seem to interpret the rivalry between Strong Bad and Tycho as this. Search "Poker Night Inventory" on Fanfiction.net or "strong bad tycho" on deviantART and you'll see.
There's possibly one-sided Ho Yay from Tycho towards Max, since he goes into very inappropriate detail asking if Max had sex with a human woman, and tells Max his sexual fantasies about giraffes, visibly disappointed when Max is squicked. This is probably less to do with an interest in Max in particular and more to do with Tycho's... animal-related interests.
Many people who hadn't heard of Penny Arcade (or at least hadn't read it) got into it thanks to this game. (Look up anyPoker Night video on YouTube, it's impossible to find a video that doesn't have a comment asking who Tycho is)
Later, in Meet The Medic, Medic refers to Heavy as his friend, with genuine fondness in his voice. In fact, a lot of Meet The Medic could potentially be a Call Back to Poker Night - Heavy's fondness for Russian Humor, birds...
In Poker Night, Strong Bad claims the next "Snake Boxer" game will have snakes with fists. Fast-forward to The Aquabats Super Show, where Matt Chapman (Strong Bad's VA, and a writer for the show), plays Carl, a blatant Expy of Strong Bad who keeps a giant cobra man with arms as a sideshow attraction.
The Scrappy: Tycho is this, big time. Even the Penny Arcade fans hated him in this game. However, he is very well-liked amongst the female players though, especially with that sexy voice of his.
Strong Bad to some players, mostly those who are unfamiliar with Homestar Runner or just can't stand Strong Bad's obnoxious attitude.
Ship Sinking: "Sascha is my only love" and Telltale's view (as stated at the recent PAX panel) of Sascha and Natascha as Heavy's girlfriends, while the gun that the Iron Curtain replaced was supposed to be "the stripper he meets in Vegas". Ambiguous, considering the game's canon status is hazy.
Tainted by the Preview: "Oh, sweet! Strong Bad, Max, Tycho and the Heavy are going to be tearing it up— wait, what do you mean it's going to be a card game?!"