Hoshi's insult to T'Pol, "Ponfo mirann", loosely translates to "Go to hell".
Three of the prominent Starfleet officers are called Admiral Forrest (Vaughn Armstrong), Admiral Leonard (Jim Beaver) and Commander Williams (Jim Fitzpatrick). These names are an homage to the three lead actors from Star Trek (1966): DeForest Kelley, Leonard Nimoy and William Shatner. One of the Vulcans from the High Command is called "Tos", which is a reference to TOS, as The Original Series is often called.
Ensign Mayweather, when discussing the transporters, says "from what I'm told, [the Captain] wouldn't even put his dog through this thing." The dog in question is Captain Archer's beagle, Porthos. Years later, in the film reboot Star Trek (2009), a surly Montgomery Scott describes his ongoing punishment by Starfleet as a consequence of attempting to prove a transporter theory correct by transporting "Admiral Archer's prize beagle," who was transported and never rematerialized.
Captain Archer jokes that the Vulcans don't think humans can flush a toilet without their help. This is an in-joke regarding the fact that restrooms of any kind are never seen and rarely mentioned in any of the Trek series. (Star Trek: First Contact (1996) has one of the more memorable allusions to bathroom activities in Star Trek.) In Star Trek: The Next Generation (1987), an eagle-eyed observer can occasionally see that in the wall display of the Enterprise-D's decks, there is only one bathroom on board.
Vaughn Armstrong, a longtime Trek actor, appears here as a human for the first time, bringing his total Trek appearances to eleven - as 9 different characters, and 7 different species (human, Cardassian, Klingon, Romulan, Borg, Vidiian, Hirogen).