The suit being decades old and increasing the wearer's strength, Hank's medical condition meaning he can't use it anymore, the banter between Scott and Hank as Mission Control, and the plot involving an aging superhero trying to stop crime at his old company who's new CEO is a younger Corrupt Corporate Executive, bring to mind Batman Beyond.
If you listen carefully, Yellowjacket's lasers appear to use the sounds of the AT-AT walkers from The Empire Strikes Back, most evident during the train sequence.
The placement of the "shrink" and "grow" controls of the suit is the same as the throttle switches for the jetpack in The Rocketeer.
Cross's mooks shooting at Ant-Man while he is running through Cross's miniature model of the building is an allusion to Zoolander. The title for this section of the score? "Center for Ants." And then, the first trailer for Zoolander 2 played before some US screenings of Ant-Man.
The bond between Scott and Ant-thony the ant and the latter's heroic but saddening demise calls Honey, I Shrunk the Kids to mind.
The Quantum Realm sequence seems to be one big one for the "Jupiter and Beyond the Infinite" sequence from 2001: A Space Odyssey. It even features closeups of Scott's face in his helmet, same as with Dave in 2001.
When Darren Cross reveals footage of the Ant-Man in action, he refers to the concept as "tales to astonish," the name of the comicbook in which Ant-Man originated.
Garrett Morris' cameo is a shout-out to his portrayal of Ant-Man in an early Saturday Night Live sketch.
A song by The Wiggles plays in the background when Hank arrives at Cassie's birthday party.