Any allusions were typically trivial, such as in "By Any Other Name" when Kirk says, "On Eminiar Seven, you were able to trick the guard by a Vulcan mind probe." That was shorthand for "move the story along." Yet in "By Any Other Name" no one became a god after passing through the barrier at the edge of the galaxy
I thought it was a nice reference to WNMHGB--and Kirk quickly blurts it out ("Yes, I know. We've been there."
), almost as if he did not care for the reminder.
nor did Starfleet benefit from the Kelvin modifications made to the ship's engines. The miracle spores from "This Side of Paradise" are never heard from again. Starfleet never made use of cloaking devices after "The Enterprise Incident." (Although Kirk did manage to make most of his crew believe that his mind was messed up.) Medusan symbiotes never appeared as helmsmen/navigators. The telekinesis from "Plato's Stepchildren" and so on.
One can argue that the incidental nature of TOS Starfleet missions meant many of the inventions or aliens would not be seen again. Starfleet, after all, is a busy organization with a primary fucntion having little to do with developing technological or biological innovations beyond first contact, so other branches of the Federeration may step in to handle the rest.