This movie contains examples of the following tropes:
Big Bad: Bladerun of the Bloodbath (血祭のブレドラン/Chimatsuri no Buredoran) is the Big Bad for this movie. A rare instance where the Big Bad of one of the two featured series is the Big Bad of the Vs. Movie, rather than a new villain. Bladerun of the Bloodbath is a new identity assumed by Goseiger's Big Bad Bladerun/Brajira.
Breaking the Fourth Wall: During the Gōkaigers' Early-Bird Cameo, Captain Marvelous introduces his Catch-Phrase by stating that since they're in a movie, they should be extra flashy. This line is omitted when the scene is revisited in episode 40 of their series.
Probably unintentionally but after Takeru defeated Juzo once and for all, he nearly fell into Gedou until his team members snapped him out of it. Here, no thanks to Bladerun of the Chimatsuri, Takeru became Gedou until Alata snapped him out of it by force who then also snapped Gosei Knight out of his own brainwashed state some time later.
Whenever a Gedoushu is slain, their second life grants them a much larger and more powerful form. So why does Shitari just flat-out die when the Gokaigers slay him? Because he gave up his second life back in Act 46 in order to give Oborojime a third life with which to defeat the Shinkengers.
Bladerun's evil plan involves using Gedō ShinkenRed's Fire Mojikara to simulate the rare solar flares needed to open a pathway to the Gosei World, the natural occurrence of which is a major plot point in Goseiger proper.
When Bladerun sends the waters of the Sanzu River up to the Gosei World, Takeru leads the Shinkengers in performing the composite characters of the sealing symbol that Kaoru was originally trained to use against Dōkoku Chimatsuri when he returned.
Chronic Backstabbing Disorder: Once again, Bladerun betrays the evil faction he worked with to further his own plans. After leading the Gedōshū under the claim of being Dōkoku's heir and inheritor to their will, he reveals that he's just using them to gain access to the Sanzu River and then flood the Gosei World with its waters.
The "same time/unison" aspect of this trope is emphasized when they are practicing, as being even slightly out of sync will ruin the effect and cause both the Gosei Card and the Mojikara to effectively cancel each other out. Without synchronization, Kotoha and Agri could only make pebbles while Ryūnosuke and Hyde just made a bit of water splash on the ground.
Early Installment Weirdness: When the Gokaigers present the Ranger Keys of the five Red Rangers, they actually call out "Ranger Key!" just as Sentai teams normally call the names of their weapons when they bring them out. They never do this in the series and this is edited out when the battle is shown again in episode 40.
Evil Costume Switch: Gedō ShinkenRed has a black vest that looks like the one he wears as a Super Shinkenger.
Hijacked by Ganon: As per usual for Goseiger, Bladerun takes the stage as the true Big Bad, once again assuming a new form and infiltrating a group of villains to use them for his own evil plans. In this case, that group of villains is the Gedōshū from Shinkenger.
Me's a Crowd: While fighting ShinkenRed and GoseiRed, Bladerun of the Bloodbath spawns two clones of himself, both in the forms he had used while working with the first two villain factions of Goseiger, Bladerun of the Comet and Bladerun of the Chupacabra.
Psychotic Smirk: Takeru sports a very unsettling one just before he transforms into Gedō ShinkenRed.