For example, the heart of the original series is the relationship between Kirk, Spock, and Bones, who are meant to be three sides of the same person. Kirk is the central decision-making part, Spock is the logical side, and Bones is the emotional side. With very little exception, Kirk always has to defer to the two of them before making his final decision, which invariably involves seducing some manner of female alien.
"No, Jim, I said a female alien!"
Except in the reboot, Kirk is just running around shooting things and Spock is a moody a*****e. Meanwhile, Bones has been absolutely replaced by Uhura, because the makers of the reboot decided that what Trek fans really wanted to see was a love triangle between her, Kirk, and Spock. Bones says a few funny things and then is barely seen. It's even worse in Star Trek Into Darkness, in which he appears in maybe three scenes.
Speaking of Star Trek Into Darkness, that installment also sought to cash in some nostalgia chips by making its central villain Khan, the fan-favorite antagonist of the Original Series episode "Space Seed" and the titular angry man from Star Trek II: The Wrath Of Khan, which is widely considered the best Trek film ever. But the character in Into Darkness bears absolutely no resemblance to the legendary villain. J.J. Abrams and crew rewrote The Dark Knight and changed the Joker's name to Khan. The one thing they did manage to keep was casting an actor who is in no way Sikh to play Khan, who is supposed to be a Sikh.
CBS / Paramount Pictures
... Yeah, neither of these is correct.