At the beginning when Barney is in the laser tag office, every high score on the board behind him says "Stinson".
You can see that Alison Hannigan (Lily) is very visibly pregnant in this episode.
At the end of the scene where Barney accepts the challenge of doing everything on the Murtaugh list, he says "OK chumps, lets do this." He then storms to the bathroom while shouting his own name in a very specific manner. This is a spoof of Leeroy Jenkins, a World of Warcraft (2005) player character. In a player made in-game movie that quickly became very famous within the World of Warcraft community, Leeroy Jenkins is in a team that's in the middle of going through a battle plan for their upcoming whelps fight in Upper Blackrock Spire. Before the leader is finished explaining the plan, Leeroy suddenly interrupts and says "OK chumps, lets do this.". He then proceeds to start the fight by charging head first through a doorway, while shouting his name in the same specific way that Barney shouts his when storming to the bathroom. Leeroy's charge ruins his team's well thought out plan for the battle, killing himself and the rest of his team in the ensuing battle.
In this episode Barney is banned from playing laser tag; however in later episodes he is seen playing again, so it could be likely that he either had his ban lifted or found a new place to play.
In the basketball game, the "teen wolf", the opposing team's best player, wears the number 23 - the same number worn by Michael Jordan and Lebron James, two of the greatest basketball players in NBA history.