For my universe:
Andorians have 4 sexes, as it makes them a far more interesting and diverse race who are slowly becoming extinct due to the complexity of their method of breeding.
Humans are a minority in Starfleet. The ship's we've seen with lots of human-looking crewmembers are the exception (even then, most of those crewmen will be of alien origin--unless specifically stated they are human).
Saavik was half Romulan, but she wasn't impregnanted by Spock, nor did she later marry him.
Despite the fact the Border Service kicks butt, they are still regarded as the red-headed stepchild of the regular Fleet.
Number One, from "The Cage", was of alien origin (exactly where is a mystery). She is of no relation to Robin Lefler.
The Romulans are the Romulans, not whatever non-canon name was created for them.
The Kzinti and the Tzenkethi are not the same species, nor are they related.
All events from Nu-Trek (even those involving 'Prime' Spock) occur across two alternate universe; the first being one where Romulus is destroyed and the second created by Nero going back in time. This means in the Real-Prime Universe Romulus remains intact.
In "Broken Bow", they didn't travel to Qo'noS, but an outlying Klingon outpost (approximately 80 hours at less than warp 5 from the Klingon Homeworld to Earth and they didn't invade?).
Troi attended a Starfleet Academy complex attached to the University of Betazed, which specialised in counselling and social sciences.
The Kes seen in "Fury" wasn't the real Kes, but rather a personification of all her negative emotions (hence the fact she was so old).
Lieutenant Arex's species are the Edosians.
V'ger has nothing to do with the Borg.
The El-Aurian homeworld was called Gallifrey