Angst? What Angst?: John Connor doesn't seem disturbed or disheartened by the news of his foster parents getting killed by T-1000. In fact, their deaths are forgotten as soon as they're revealed.
Award Snub: James Cameron was so impressed with Linda Hamilton's performance and her dedication to the role (she lost twelve pounds during filming because of her aggressive training regimen) that he campaigned for her to get a Best Actress nomination. He was unsuccessful.
Draco in Leather Pants: As noted below, Sarah gets toted as a paragon for feminism and an excellent role model by a lot of fans. This ignores that she now has a Hair-Trigger Temper, has been sectioned because of how dangerous she is and is prepared to murder an innocent man over something he hasn't even done yet. She essentially borders on Villain Protagonist. James Cameron even said she wasn't meant to be a role model. To Sarah's credit, she does have a Heel Realization.
Even Better Sequel: T2 is commonly held to be one of the best movie sequels of all time, and many fans prefer it to the original.
Fan Nickname: In the early days "Liquidator" was sometimes used as the moniker for the T-1000, but it never really stuck and today it has fallen into disuse.
Watching Sarah Connor struggle with her emotional instability is a lot harder in light of Linda Hamilton later admitting to suffering from bipolar disorder in real life.
John Connor mentioning that the Russians are "our friends now." Wait until 2014!
James Cameron first thought of casting Michael Biehn as the T-1000, but ultimately decided that Kyle's actor now being the Terminator would be confusing. Cue Terminator Genisys, and John Connor himself becomes a shapeshifting Terminator.
Jeanette Goldstein, codifier of Vasquez Always Dies, gets killed off again here (and she would again in Titanic (1997)). So Vasquez always does die, even when she's not Vasquez.
Michael Biehn nearly got brought back as the bad guy. He was normally typecast as villains, and his roles with James Cameron were the rare times he got to be heroes. In his next collaboration with Cameron - The Abyss - he would indeed be the bad guy.
It Was His Sled: The T-800 is the good guy in this film. Trailers and promotional materials went to great lengths to hide this twist, but it's one of the most well-known parts of the film these days. In fact, some people who go back and watch the first film are surprised that the T-800 is the villain there.
Jerkass Woobie: Sarah Connor is not exactly the most pleasant person in this film. A harsh, militant woman who barely gives the son the affection he needs and nearly murders an innocent man over something he hasn't even done yet. Given everything that she'd gone through before, it's easy to see where all of that came from.
Misaimed Fandom: An examination of a woman nearly losing her sanity and humanity due to being burdened with terrible, unfathomable knowledge is often mistaken for being a good mother and heroine.
Narm: John's "acting human" lessons have really not aged well.
Nightmare Retardant: The T-1000's glitches in the Special Edition. In fact, this trope was the entire reason Cameron left it out of the original theatrical release, as he felt that it distracted from the tension of the film. Part of the draw of the movie, as many professional critics noted, was that audiences weren't able to figure out—right up until the end—what could actually hurt the T-1000.
One-Scene Wonder: Michael Edwards has less than a minute of screentime, but his appearance as the adult John Connor in the prologue has remained a favourite of fans.
Minor example, but a good eye can spot when Leslie Hamilton-Gearren is being used as a double. In contrast to the military-esque training routine Linda Hamilton was on, Leslie only had to "hit the gym for a few hours a week". So the difference in body types is noticeable.
Visual Effects of Awesome: The T-1000 completely blew the audience's minds when Terminator 2 came out, and still looks amazing today. Terminator 2 and Jurassic Park are credited for the CGI revolution.
Woolseyism: The famous line "Hasta la vista, baby!" became "¡Sayonara, baby!" in the Spaniard dub. It became just as popular in Spain as the original in America.