The new Naked Gun has one subtle reference that doesn't point back to the original film trilogy, but much further - to the TV series that served as the blueprint for all three movies. In other words, it's a nod to Police Squad! from 1982.

In the final scene of the new film, everyone around the main characters suddenly freezes, while the protagonists themselves are confused about what's happening - yet they're still able to move:

This is a direct callback to the endings of every episode of "Police Squad!". That exact gag happened each time - for example, here's how episode two ends:

The two brothers from the famous Zucker-Abrahams-Zucker trio - had their mother, Charlotte Zucker, appear in a bunch of their films. Though her roles were mostly brief and cameo in nature, if you enjoy the spoof comedies of that era, you're sure to remember this elderly lady.

In the original "Airplane!", Charlotte Zucker tried to apply makeup.

"The Naked Gun: From the Files of Police Squad!": she played Dominique, the secretary for the mastermind villain.
“I must kill Papshmir.”

Remember that memorable interrogation scene on Pier 32 from The Naked Gun?

The actor who played the sleazy dock foreman is named Joe Grifasi.