With the new movies, I wish they'd just do all new stuff.
My problem with Into Darkness was how much it kept reminding me of TOS, often in an unfavorable way. I mean, I'd be totally cool with new versions of the same characters in an alternate timeline, but I don't like that they kept reminding us of TOS by having Spock Prime show up, by all the similarities to TWOK, etc. It kept me from really accepting the characters as different versions, and that made me keep comparing them to TOS and TWOK in an unfavorable way. And I know it's an alternate timeline so things happen differently, but I wish they'd focused on them having totally different stuff to deal with.