What easter eggs or references would you love to see in STID or a future Trek film? Personally, I would love the Kzinti or Slavers mentioned, a line or two of dialogue that would indicate Prime Kirk lives potentially by canonizing elements of the Star Trek: Odyssey trilogy, a few details about the Prime Captain Robert April, and something that would identify the Prime George Kirk as the first first officer of the Prime USS Enterprise (NCC-1701).
Just once I'd really like to see McCoy beam down to a primitive planet and say: "Behold, I am the Archangel Gabriel!" Why not, right? It's not like they'd know WTF he's talking about.
How would the characters know about or mention the prime universe's characters? Beyond Spock Prime? The JJ Universe's April features in IDW's "Countdown into Darkness" comic mini-series.
You gave the answer: Spock Prime or at least information he gave. Another possibility would be a Starfleet vessel crossing over from the Prime universe/reality similar to how the USS Defiant seen in "The Tholian Web" crossed over to the Mirror Universe.
I don't expect this new movie to spend any time reminding people there was a prime universe. I'd be surprised to even hear a namedrop for Nimoy's Spock. Why confuse new audiences?
I can't say there is anything in particular I have a desire to see, as far as easter eggs or references go.
Two things: 1) I asked in the OP about easter eggs and references for not only STID but future movies as well. 2) That info could merely be visible on a computer screen seen in the background and thus probably wouldn't even get much notice until the movie comes out on dvd and then it still might not get noticed.
Maybe McCoy could give a passing hello to an Olympic gymnast he hooked up with just before entering med-school?
Here's one: An unnamed and slightly drunk Starfleet Lieutenant doing a 23rd-century version of Karoke at a bar... ...and singing "I'll Take You Home Again, Kathleen".
Salt and pepper shakers in sickbay. As the ship is under attack, and damage reports come in to the bridge from all over the ship during the chaos, we can clearly make out a voice saying, "Gravity is down to point eight."
One very meticulously timed "Ohhh Myyy!" ETA, thought of another: In whatever pub scene that is sure to show up, have Brent Spiner and Tony Daniels sharing a pint in the background.
I'd like to see a classic TOS Constitution Class ship parked in the background somewhere as a derelict.