Discussed in-universe when its found out that in order to make a Super Saiyan God you need six benevolent Saiyans pure of heart, with one receiving energy from the other five, Roshi brings up the fact that while Goku is a nice guy his intense love of combat brings his benevolence into question. Piccolo outright scoffs at the gang's chances, thinking they only have two pure-hearted Saiyans around in Gohan and Goten.
Is Beerus really as evil as his status as antagonist suggests? Let's take a look at his crimes: He humiliated King Vegeta in front of his son, and tried to blow up Earth.Pretty evil stuff. Except... Harsh as it may sound now, King Vegeta was also a HORRIBLE individual and his son wasn't much better at the time so that bit of humility was well deserved. As for destroying Earth, sure Beerus SAYS he's going to, yet he constantly keeps delaying, holds back his power in order to train Goku during their fight, and even decides not to destroy Earth in the end. One wonders if he was ever really serious about it in the first place. Also, he did destroy some planets, but it comes out more like a sort of orange morality. Sure, the reasons he does it are a bit petty, but he's a God of Destruction after all, so destroying planets it's kind of his thing, and it's not driven by malice or hatred. The sequel even confirms him as a True Neutral.
Beerus. Some people thought having the God of Destruction at the top tier of the power scaling hierarchy was fitting, since the Saiyans. Others find him far less interesting than other antagonists, as well as being annoyed by his jerkish attitude and how he get away with anything as there's no one to put him in his place.
Whis too. While he normally lets Beerus do whatever he wants, he will step in if Beerus does take things too far in the uncut version of the movie, Whis dope slaps him after he goes on a wasabi-filled rampage, then stops him from going back to destroy Earth by basically telling him to sit down and eat his sushi. His obsession with food and effeminate nature also divides the base. The fact that he was (at that point) the strongest character in the franchise, but is so different from all of the other "top tier" characters had mixed opinions.
Super Saiyan God. Some fans find it interesting while others lazy, and just an excuse to create yet another Super Saiyan form for merchandising purposes.
The movie in general goes through a case of Love It or Hate It. Fans notice how it feels like classic Dragon Ball due to its focus on comedy rather than drama, combined with elements of Dragon Ball Z, such as only Goku, Vegeta, and their relatives having any sort of role.
As a side effect of Super Saiyan God, there's also the matter of "Super Saiyan 4" getting retconned. Although many fans consider the events of Dragon Ball GT to be Canon Discontinuity anyway since Akira Toriyama had little involvement in GT, as well as the fact that movies always seem to have continuity issues with the main anime. But then again, this is one of the few movies to be considered "canon" as it got adapted into an anime and a manga.
Crazy Awesome: Beerus. Used King Vegeta's head as a footstool in front of his own son Prince Vegeta while making him treat him to an Eight-Course Banquet, curbstomped Super Saiyan 3 Goku with a single chop on the back of the neck, used chopsticks to defeat Tien and knock Piccolo out with pressure point attacks, defeats Super Gotenks by spanking him, effortlessly defeats Vegeta with a single pressure point attack to the forehead and also one shot all the other Z-Fighters including Android 18, Ultimate Gohan and Majin Buu. Oh, and he also needs the sounds of multiple bombs exploding continuously and simultaneously just to wake up.
Ensemble Darkhorse: Beerus is becoming this for being a likable and humorous antagonist despite his childish motivations. Even many of the film's detractors say he was a bright spot on the film.
"Funny Aneurysm" Moment: Goku jokingly stating that a villain slapping Bulma to get Vegeta stronger becomes cringeworthy in Dragon Ball Super, where a villain kills Future Bulma, traumatizing Future Trunks as well as pissing Vegeta off enough that the latter finally goes into Tranquil Fury.
Germans Love David Hasselhoff: No matter what way you look it, the numbers that the movie did in the Latin American countries is nothing short of remarkable. As seen here, in some countries, it debuted as the #1 movie in the box office. That's a major achievement for Short Anime Movie based an franchise that is nearly thirty years old and hasn't had a movie since 1996.
Harsher in Hindsight: In the anime series, Vegeta wanted to destroy Mr. Buu because he saw him as just one more disaster waiting to happen. If he had destroyed Buu then and there, Beerus would have been able to sample some pudding and not threatened the Earth. This is later subverted as, if Beerus did leave peacefully, Goku would have never achieve Super Saiyan God, impress Beerus and Whis, and would have been very underprepared for the events of Dragon Ball Z: Resurrection ‘F’.
Internet Backdraft: While Battle of Gods was a relative success, there are some fans who had issues with the film. Mainly having to do with the fumbled continuity of character ages, Videl's convenient pregnancy, the Mai/Trunks Ship Tease, Super Saiyan God form, and that the movie is supposedly canon.
It Was His Sled: By now, it's pretty common knowledge that Beerus is the first villain to truly defeat Goku since Cell.
The way they get Goku into Super Saiyan God Mode is getting all the Saiyans to take hands and form a circle. Crowned with getting Videl into the Ring-a-Round Rosie because she's pregnant.
Visually speaking, Super Saiyan God Mode itself is also not that impressive: It's just Goku with pink/red-velvet hair and lighter eyes with a different color glow. Some fans alleged that Toei just wanted to sell off surplus Dragon Ball Kai merchandise, and the easiest way to do so was with possibly the laziest Super Saiyan design ever. Possibly lampshaded by Piccolo's reaction.
The official name of Goku's new power up? Super Saiyan God Super Saiyan.
Never Live It Down: Beerus's desire for pudding is swiftly becoming his defining trait among some fans.
Special Effect Failure: The CGI in the final battle scene is very noticeable. At best it can be looked at as Narm or as a poorly done attempt to string an action sequence together.
Squick: As mentioned under crack pairing, Trunks is canonically 12-years old in this film while Mai is at least 46. Even though she is de-aged, the Ship Tease can come off as this.
Take That, Scrappy!: For fans who don't care for Buu or Gotenks, watching Beerus utterly curb stomp them in hilarious ways makes for a fun moment.
Videl's pregnancy could have been used as a Character Development arc for Gohan (and in some extent also how it could have affected Piccolo or Goku's character at the prospect of becoming a grandfather) instead of being just another Plot Convenience.
Even Vegeta's character arc could have been explored, since we can see how personal his fear of Beerus is, instead of just being told about the potential danger he is for any world in the Universe.
Basically every popular voice actor from the All Star cast reunited for the film. Then only 20% of the cast get any dialogue.