Is Cooler Cannon or not?
Cooler's Revenge is one of the few Dragon Ball Z movies that can be placed in the series timeline without serious problems. The events of the movie could be placed between episodes "Z Warriors Prepare" and "Goku's Ordeal" of the Trunks Saga, while the Z Fighters were training for the arrival of the androids. In the book Daizenshuu 7, the movie events are placed chronologically in this period, around years Age 764-767. In the video game Dragon Ball Z III: Ressen Jinzōningen, Cooler and his henchmen also arrive on Earth during this period, and the debriefing prior to the "Strongest vs. Strongest" stage in Dragon Ball Z: Budokai Tenkaichi 3 asserts that Cooler's Revenge takes place following "[Goku's return] to Earth after crushing Frieza", somewhat confirming this. In addition, Cooler's final form was stated to have a power level of 470,000,000 in an issue of V-Jump, which far outclassed Frieza's power level of 120,000,000 in his final form. The fact that Goku was able to easily defeat Cooler's final form in his Super Saiyan form strongly supports that the movie took place during the three year training period, as Goku's power level during his fight with Frieza was 150,000,000 (in Super Saiyan form).
However, there are several minor facts that disturb the canonicity of the mainstream series. To begin with, in spite of Future Trunks killing both King Cold and the revitalized Mecha-Frieza only hours prior to Goku's return to Earth, Cooler seems intent only on seeking vengeance for the shame thrust upon his family by Frieza's display of inferiority on Namek, as though he were completely unaware of not only his father's recent death, but also of the second defeat (and actual death) of his brother, as well. However, it is entirely possible that news of these recent events never reached him, since Future Trunks, along with killing Frieza and King Cold, blew up their spaceship and killed all of King Cold's men. However, the video game Dragon Ball Z: Supersonic Warriors does mention King Cold's death as well.
Gohan has a tail in the film, despite not having one during the time in the series when Cooler's Revenge is purported to take place. This is not unheard of in the mainstream series, however, as Gohan's tail regrows twice within just twenty-one episodes of the first time his tail is removed by Piccolo in "Gohan Goes Bananas!" (in the edited Ocean Group dub, there is a 7-episode difference between "Gohan's Metamorphosis" and "The End of Snake Way"). In addition, Goku was shown to easily transform into a Super Saiyan upon his return to Earth, but in this movie he only transformed right at the end of the battle. However, it is shown that Goku didn't really need it throughout the battle, and at this point in time he only used the Super Saiyan transformation as a last resort. This is kind of like how Gohan had unlocked Super Saiyan 2 after fighting Cell, but only used it as a last resort against Bojack in the movie Dragon Ball Z: Bojack Unbound.
The transformation happened as a result of anger, similar to when he transformed on Namek. It is possible that the movie was written before the Trunks Saga, so it was assumed that Goku killed Frieza, but also that the transformation to Super Saiyan could only be achieved through intense anger and not controlled once achieved (after a bit of practice according to Goku). It could also have meant to be a movie alternative to the Frieza Saga and was done purely for dramatic effect.
The events of The Return of Cooler must be set between the episodes "A New Guardian" and "The Games Begin" of Dragon Ball Z, during the wait for the start of the Cell Games. Additional proof is found in Dragon Ball Z: Supersonic Warriors 2, where the Z Fighters go to New Namek and confront Meta-Cooler right before the Cell Games. The movie's major plot hole is that Dende is Guardian of Earth at the beginning of the movie, by which time Gohan could turn Super Saiyan, which he appears incapable of doing in this film. Gohan is clearly younger than he was in the Cell Games, because his hair is still long and he is still shorter than Krillin. Also, Goku and Gohan did not power down from Super Saiyan form from when they left the Hyperbolic Time Chamber in the anime/manga until after Cell was destroyed, but they are seen in their base forms in this movie.