Kaizoku Sentai Gokaiger vs. Space Sheriff Gavan: The Movie provides examples of the following tropes:
Acting for Three: Kenji Ohba not only reprises his role as Retsu Ichijouji (Space Sheriff Gavan), he also reprises his two major roles in Super Sentai, Shirou Akebono (Battle Kenya) from Battle Fever J and Daigorou Oume (Denzi Blue) from Denshi Sentai Denziman. And of course, at the very end the three of them are standing together on-camera, with Daigorou's arm resting on Retsu's shoulder. For those who don't know, that is a VERY difficult shot to do, since they were filmed outside and not in a green screen studio.
The Alcatraz: Part of the setting, with the Gokaigers even planning a breakout.
Aside Glance: Upon defeating the Gokaigers, Gavan salutes at the camera.
Book Ends: A shot of Gavan at the top of a flight of stairs.
Combination Attack: Gokai Red and Gavan execute a finishing attack on giant Asurada called the Gavan Marvelous Dynamic — Marvelous plugs the Gokai Red Ranger Key into his Gokai Sabre for a Final Wave and does a powerful slash while Gavan uses his Gavan Dynamic, a powerful slash from his Laser Blade.
Continuity Cameo: Well there's obviously Gavan, along with Battle Kenya and Denzi Blue. Several past Super Sentai villains appear as well.
Hope Spot: The beginning of the movie has the Gokaigers believing they shot down Gavan's ship that was chasing them, until Electronic Starbeast Dol flies out of the flames and takes them down.
I Owe You My Life: Marvelous helps Gavan to return the favor, since Retsu saved a young Marvelous and helped make him the man he is today by teaching him to be brave. The other Gokaiger go along because, as they say, Marvelous' origin is their origin, so by association they owe him too.
Name's the Same: Gokaiger's Don and Don Horror, the Big Bad of the original Space Sheriff Gavan series. Although Don Horror doesn't appear in this movie, when Makuu Chief Asurada says that the blood of Don Horror is flowing through him, the Gokaigers lampshade this, saying they don't know who Don Horror is but their Don is more impressive, though Marvelous says that doesn't really matter either.
While discussing Gavan, Denzi Blue mentions to Battle Kenya that he met him once. An off-screen Denziman/Gavan teamup perhaps? This is more likely a Lampshade Hanging of the aforementioned Acting for Three trope.
Jerashid is one of the inmates in the Makuu Prison. Since he had retired from villainy earlier in the series, it's unclear what led to his imprisonment. He even starts to explain, but the Gokaigers blow him off.
Overly Long Gag: The time Don takes to recover from a fall, in slow-motion.
Production Foreshadowing: In the Go-BustersEarly-Bird Cameo, Basco assumes they are "Super Sentai wannabes", before they reveal themselves to be the 36th Super Sentai team. Hikonin Sentai Akibaranger, an unofficial Super Sentai series which follows the adventures of an unofficial Sentai team trying to get their own TV show and be recognised as an official Super Sentai, first aired a few months after the movie was released.
Theme Song Power Up: The Space Sheriff Gavan and Kaizoku Sentai Gokaiger main themes play during the Gavan vs. Gavan Bootleg/Gokaigers vs. Asurada double battle near the end of the movie. Also, the Gokaigers and Gavan quote their own theme songs at various points during the movie to inspire or motivate themselves/others (such as Gavan's pep talk to a young Marvelous).
Time-Shifted Actor: Averted; Kenji Ohba plays Retsu in Marvelous's Flash Back, but they only ever show him from the back or in distant shots (and apparently touched up the gray out of his hair) in order to hide his age.
Transformation Sequence: According to the narrator, it takes one-twentieth of a second for Retsu to change into Gavan, while the Gokaiger only take one-tenth of a millisecond to transform.
Ungrateful Bastard: Played for laughs; Gai gets manhandled by Luka and Don because of how late his rescue attempt was.
Visual Pun: Gavan slashes at the screen in a certain pattern once the "cross"-over part was mentioned in the narration.