The Gokaigers are essentially what Aka Red was during Gogo Sentai Boukenger's anniversary special, that is being able to turn into a past ranger. As of #2, this has gone beyond just a Mythology Gag and is actually a key part of the plot, as Aka Red is the source of the Gokaiger powers. And as of #15, Aka Red is indeed revealed to be key to the plot, as he is the leader of the Red Pirates himself.
During the big Gokaiger fight scene in #1, Don makes use of a trapeze swing in the middle of the ruined city, seemingly hanging from nowhere, just like the one Kai had created in episode 3 of Mahou Sentai Magiranger.
Navi isn't the first supporting character in a Sentai show to quote previous shows - that would be Bakuryu Brachio.
At the beginning of #2, Navi asks the pirates, "What do we do? What do we do? What would you guys do?" ("Dousuru, dousuru, kimi nara dousuru?") This was a line from the ending theme of Denjiman (Although the actual lyrics have "dousuru" repeated 3 times.)
He says it again in episode 6. In the same vein, Nanonanoda's reaction to seeing the JAKQ Hurricane is a variation on a line from JAKQ's theme song: "Spade dia(mond) heart clover(club), hey hey hey!"
Also when fighting Gokai Yellow transformed as Vul Panther, Nanonanoda references Sun Vulcan's second ending theme:
Nanonanoda: Ichi tasu Ni tasu... Ichi tasu Ni tasu?! translation "One plus two plus... one plus two plus?!" Gokai Yellow: Sun Vulcan! note In Japanese, "three" is "san", pronounced the same as the English word "sun".
Ahim recites catchprases of Karen Mizuki ("Do you want another?") and Peggy Matsuyama ("Are you ready? Here I go!''") in episodes 12 and 13, with her own polite speech spin on them.
Another from #2: look very closely when the team is surrounded by numerous people are dressed in black. Right behind a pair of nuns... is a kuroko.
A mall in #4 includes signs for several businesses from previous series, most notably SCRTC and Tomorrow Research.
Literal Giant Mooks were habit in Shinkenger, though having the Giant SuGormin transform into support mecha is a concept normally saved for our heroes.
In episode 8, Captain Marvelous declares, "Stop the Battle!" in Gratuitous English before starting the team's Finishing Move. "Stop the Battle" was the name of Goggle Five's ending.
Episode 10 contains several references to JAKQ's opening, including Luka's card shuffling and the 5 cards that fly onto the Monster of the Week.
Gokai Silver was given his powers by Dragon Ranger, Time Fire, and Abare Killer; and his GoZyuJin mecha homages all three: the V-Rex (saurian sixth mecha in among an otherwise vehicle-based set) and Time Jet (its Drill Tank mode), AbarenOh (its tail becomes a drill arm) and BakurenOh (the same plus a purple/blue color scheme), and a combination of DaiZyuJin and Dragon Caesar thrown in the design (especially the drill tail and GoZyuJin's head being basically DaiZyuJin's tweaked as an anchor).
Insarn seems to be a little smitten with former Red Racer Kyousuke Jinnai. Of course, she wasn't the first...
Although this time, it seems to be a little bit one-sided on her part...
From the same episode, we get a little insight into Navi's predictions, as he dreams he's an Engine.
Also from #14, the Gokaigers turn into Turborangers before Kyousuke informs them that they're the wrong keys. This was a reference to the fact that both Turboranger and Carranger are car-themed, a fact that was already commented upon when Carranger was announced.
Kyousuke gives the Gokaiger bottles of Coffee Milk, the favorite drink of VRV Master.
And Zealousto uttering "Honoo no Jealousy Power!" sounds a lot like the rollcall from Goseiger.
#17: When told to activate Treasure Navigation, Navi says "Tonde-kurukuru, sugoi yatsu", which was the very first line from the DaiRanger ending.
After Gai transforms into Gokai Silver for the first time, he gives off a rather long solo roll call going through each of the other Gokaiger's colors, and in the numerical order of the Gorangers, to boot.
Gai also does the Zyuranger transforming motion after switching to GoJuuRex.
The Picture Book that Gai has in episode 20 is the book that was drawn by Yuuta's father from the Go Go Five vs. Gingaman movie
Don gives a box of donuts to Ryōma as a thank-you present for saving their lives in episode 20. This is a reference to Hikaru's favorite snack.
Basco's pet monkey Sally resembles Zulten from Kousoku Sentai Turboranger, what with his color scheme (red/black/silver), general annoyingness, and being a squat bipedal lackey for the bad guys with functionality in their bellies.
Probably unintentional, but the ambulance used by Tatsumi Matsuri in #23 is the archetype that her old mecha, the Pink Aider from Victory Robo, was based on.
More likely intentional, in order to underscore the fact that Luka and Ahim were like big sister/little sister, during their fight against Zangyack to protect the taxi, they transform into their counterparts from Chikyuu Sentai Fiveman and Mahou Sentai Magiranger. The episode itself was an homage to Rescue Sentai Gogo Five. All three shows featured siblings as sentai teams.
Also in #23, when Basco tries to siphon the GoGo V power from Matsuri, nothing happens. After a brief fight, it's revealed that it was Ahim, in MagiPink form, who stood in for her. Makes sense when you remember Houka's magic power was self-transforming (except there are no pink bows involved this time...).
In #25, Nanami, now an actress, is seen reading her lines from a script titled "Ima Kaze no Nakade" ("Now Inside the Wind"), the name of the Hurricaneger ending theme. To add to that, the song you heard playing in the radio of one of the victims? That was a song sung by Nanami as early as episode 2 in Hurricaneger.
In #26, Don winding up with a tree branch as a weapon may have been a dig at the fact that many past green Rangers have been drawing upon plantlife for their powers, like ShinkenGreen and MagiGreen.
Also in #26 during the big battle, Gai says "Prepare...prepare...prepare yourselves!" ("Kakugo...kakugo...kakugo shirou!") These same lines are part of the Hurricanger theme song — and if you hum along to the BGM, he hits it at almost the exact same time as it would be on the theme song itself.
When the Hurricangers give their Ranger keys back to the Gokaigers in #26, Yousuke acknowledges them as "legendary successors." This was the motivation for the original Hurricanger team, as they wanted to live up to the legend.
Also in #28, at one point when they're searching for the Jetmen, you can hear Gai singing the beginning of the Jetman OP theme. Nice to know it showed up somewhere in the episode...
In #29, Yukito Sanjo says "The more you rampage, the stronger you'll become" ("Abareta kazu dake tsuyoku nareru"), which was a line from Abaranger's opening lyrics.
Even the music has this. The extended version of Gokaiger opening contains a tune similar to the first tune of Goranger's opening theme.
Gao GokaiOh bears a resemblance to the final mecha of the Gaoranger team, GaoKentaurus.
The young scientists in the Academia releasing two light butterflies mirror the first scene of the opening sequence of Choujuu Sentai Liveman.
Also as an Actor Allusion, the Monster of the Week, Zcien, is a scientist type who is voiced by Joji Nakata, who played Liveman's antagonist Great Professor Bias. He even states before the giant mecha battle "The word 'defeat' is not in my vocabulary!", which was Bias' catch-phrase.
One of Zaien's captives in Episode 30 has Green Sai's rugby uniform on, with black stripes as a nod to Black Bison.
Ahim's quick costume changes in #29 are a tradition among Sentai heroines.
When they transform to the Livemen in Episode 30, the CGI grid animation takes the form of the original Livemen's poses.
Gai does karaoke again during Episode 36 as the Go-On Wing, busting out a line from the Go-Onger theme song.
KanzenGokaiOh features missile-shooting fingers and a Rocket Punch, both often-used weapons in many past sentai mecha. It's worth noting that Denji Sentai Megaranger, which spammed the rocket punch usage with Super Galaxy Mega, gets a tribute ep the following week.
KanzenGokaiOh's movement already brings to mind EngineOh G12 and other such final mecha that wind up crippled from their own size, and slide around rather than walk. Ironically, KanzenGokaiOh's has some of the least number of parts for a final mecha - the GokaiGalleon, GoZyuJin's arms, with the rest being Machalcon.
The Great Walz resembles Dora Talos from Kyoryu Sentai Zyuranger and it being given to Warz Gill by his father is like how Kai, Bondora's son, got Dora Talos. Like Kai, piloting the mecha lead to Warz's death at the hands of the Sentai team's ultimate Mecha.
Gai says "Gokaiger Win" in the Megaranger episode after bringing down two of Basco's droids; where a similar phrase would appear on screen in that series.
And "Time Up" in the Timeranger Episode after taking down one of Matrintis' droids; where it was used by said team in their own series.
Zatsurig, the Action Commander of #41 (who turns out to be responsible for destroying planet Famille and killing Ahim's parents), uses an Evil Eye with Green Lantern Ring abilities to fight, not too different from Wolzard.
In #45, Ninjaman admits that he was sealed in the bottle following an incident 10 years ago, where he attacked escaping zoo animals. Look carefully at the animals - a lion, tiger, gorilla, elephant and alligator. All of which had prominent roles in Hyakujuu Sentai Gaoranger exactly ten years ago.
In the same episode, the Gokaigers turn into a group of lion-themed Rangers to test Ninjaman's knowledge. When he guesses correctly, Joe (who has turned into Go-on Blue) utters "zubari seikai" ("just correct"), Renn's (the original Go-on Blue) Catch Phrase.
In #49, the Great Insarn shields itself with a seemingly impenetrable force field, just like Queen Ahames in Dengeki Sentai Changeman. Ironically, the Gokaigers manage to break through it by using said team's greater power.
The Flying Ghost Ship has a very subtle one when Marvelous alone turns into Red Hawk while the other four turn into four Dekarangers - Jetman started out with only the Red senshi while Dekaranger did the opposite, with Red joining last.
Also in Gokaiger vs. Gavan, when Retsu Ichijoji gives the opportunity for the Gokaigers to escape, he says "Farewell tears, hello courage!" It's a line from the theme song of the original Gavan series. In doing so, he gave Marvelous a hint as to who saved him when he was a boy. This would ultimately serve as Marvelous' motivation to rescue Gavan when he was ultimately captured and taken to Makuu Space.
And yet another from Gokaiger vs Gavan: Gavan was played by Kenji Ohba, who also played two Super Sentai Rangers - Battle Kenya (of Battle Fever J) and Denzi Blue (of Denziman) - so, of course, Battle Kenya and Denzi Blue make an appearance, and are key to helping Gavan.