In the first season, Rai was an absolute beast who had mastered his teammates' techniques and always won easily before his match with Rei and Takao. But in G-Revolution, he's overly emotional, drives himself way too hard, and in general is just nowhere near as impressive.
Judy is one of the key figures in defeating Borg in Season 1, organizing the project to get Takao a better blade for his fight against Yuriy and rounding up the remaining bladers with bit-beasts to act if Takao loses after all. And before that, she already showed herself as is a hardworking, talented, dedicated, and no-nonsense woman of science. Come Season 2 and she can do as good as nothing without the Bladebreakers' help and guidance, and also happens to be redesigned with a more generic pretty face than she has in Season 1.
Rei's match against Moses is a subject of heavy debate among the fandom. The Ass Pull victory granted to Moses (a rock from the stadium's remains hit his beyblade and let it stay in the Stadium while Driger MS lost by stadium out) is either a Heartwarming Moment as his love for his sister pushed him through the battle and allowed him to win, or a cheap victory awarded to someone who really didn't deserve the victory as he did pretty poorly against Rei, who dominated for the majority of the fight.
The art design and character designs changed every season. Which season looks best is a matter of debate.
For the longest time since the first season's American Tournament, it was "common knowledge" that Max's parents are divorced, despite their lovey-dovey behavior during the Russian Tournament. The idea has largely been abandoned, but there's still people who believe it here and there.
Sergei's last name is not "Petrov". That's fanon created because he was the only one of Borg without a last name. This "knowledge" will likely disappear now that Rising gave him a canon last name.
It's always taken as fact that Yūya Minami dies after his usage of Digital Bird in the Japanese version of Season 2. This is never said nor implied. Firstly, the moment of his death is taken as being immediately or shortly after the fight, but that doesn't match with the fact Kai hallucinates Yūya in hospital clothes. Secondly, the wielder of Digital Dragon, Garry, makes a cameo in S3E5. And if he got better, there's no reason to assume Yūya didn't.
Because someone once put it on Wikipedia and nobody bothered to check the sources (that the original editor provived), it is thought that the members of the Ming-Ming Band and of the BEGA Training Squad are called Hikaru, Jelly, Killy, Billy, Gray, and Hawk. They aren't. Their names are Chiru-Chiru, Tam-Tam, [unknown], Keizō, Gamarra, and Izam.
Mao. The most popular female character by a long shot. So much so that she was one of the first characters to make a return in the Bakuten Shoot Beyblade: Rising manga, long before the rest of her team not counting Rei. She may have also become a favorite of Aoki himself, judging by his art gallery.
Dizzi, especially since she was only exclusive to the dub. When she disappeared in G-Revolution, fans were disappointed by this decision.
Bianca and Rosetta, being two cute girls in a show that doesn't have many, are very popular for characters that appeared only in two episodes.
The English dub's atrocious one-liners and puns have a more humorous charm when you hear Rei say one in Carlos'svoice (they are both voiced by Daniel DeSanto).
Gordo looks a lot like Android 16 from Dragon Ball, which is funny enough among some other DB-esque designs like Team Psychic's trackers. But in 2014, Akira Toriyama revealed that Android 16 is modeled after Doctor Gero's dead son. This makes the Zeo-Gordo team-up all the more appropriate.
Takao. Yes, he can be a self-centered, arrogant jerk for quite a number of times but you can't help but feel for the guy in G-Revolution since it's revealed he felt alone after his teammates left him to join other teams and even suffered from Heroic BSoD as a result of their abandonment.
Kai. He may be evil and power-hungry in the first season but it was revealed that he was raised in Volkov Abbey, where he would undergo strict training and huge discipline for simply losing. He also suffered trauma from the power of Black Dranzer after attempting to use it, which changed Kai forever.
The manga reveals that Kai's father abandoned him as a child for beyblade which in turn made him hate them and becoming the cold character he's known for.
Macekre: Nelvana, already known for sterilizing another popular anime series, more or less did a 4Kids-level job with Beyblade, ranging from changing and Americanising many of the names from characters that are obviously not American, to changing plotlines and plot points, and adding the unnecessary and often annoying characters Dizzi, AJ Topper, and Brad Best. They also used the same opening theme for all three series (said opening theme is actually popular, though).
Narm/Narm Charm: Unsurprisingly, the series is absolutely dripping with it. From the Serious Business of the beyblading itself, to the overly-dramatic and hammy acting (especially from the dub). It's doubtful the fans would want it any other way.
Hiromi gets this reaction due to being a girl who by the looks of it was created just to add a female protagonist to the anime. The problem of "just" is that she wasn't a blader, which really ground some people's gears, and all-around lacked a defined role in the team. The writers had no idea what to do with her besides making her the token girl, so she ended up as good as mobile decor by the third season. She never lives up to the full potential of The Chick, namely being The Heart, possibly because that already was Kenny's role.
Daichi is subjected to this for "stealing" the spotlight from the rest of the cast.
Ming-Ming could very well be the biggest scrappy of the series, especially in the dub. Her singing (in the English dub), her pop star status, her constant attention hogging, as well as her condescending personality towards the BBA (especially Hiromi) are usually the target for her hatedom. You'll be hard-pressed to find anyone who likes Ming-Ming.
Snark Bait: Since its premise is "Save the world WITH SPINNING TOPS!!!1!" and it's not acting the least bit self-conscious about it, the whole franchise is a frequent target of mockery.
They Changed It, Now It Sucks!: Subverted. There was considerable initial dislike for the new art style featured in the second season as well as the subtle changes in personality the characters exhibited (e.g. Takao losing all his character development), but the second season's story arc was recieved as much less formulaic and overall more interesting.
The Bladebreakers come off as this in the episode "The Power Half Hour!!!" when they give Takao huge scorn for modifying his beyblade. In a series where the Bladebreakers modify their beys all the time (both before and after this episode), it makes them hard to sympathize with and come off as massive hypocrites.
Hell, in the next season, they've designed an entirely new system instead of just getting resources from the other teams who still had the current system (even with BEGA taking over).
In the episode "Take Your Best Shot!", Rei telling Rai that he should've been more upset about his loss, only to tell Rai to calm down about his loss in a later episode rubs some people the wrong way.
Viewer Gender Confusion: There are a few male characters who are likely to be mistaken for female before speaking or being spoke about. Suzuka, Hikaru, and to a lesser extent Olivier and Denny all qualify.
What Do You Mean, It's Not Political?: When you consider that the Majestics' biggest issue is a lack of team spirit, the Europe arc reads a bit like a commentary on the lack of true unity among the member states of the European Union. This view is helped by the fact that each Majestic comes from a different country belonging (or that used to belong) to the EU.
The Woobie: Whilst a lot of characters have their spotlight as this, these characters are arguably the biggest woobies in the series.
Rei can be seen as one after his battle against Boris.
Minami. Yes, he can be somewhat of a nuisance towards Kai but he's simply an average kid who looks up to his idol and wants their influence to make them stronger. What really sets him as a woobie is S2E16, where he was recruited by Team Psykick after being rejected by Kai in hopes of surpassing him. This meant he was used by the team and had the misfortune to tame the cyber bit-beast, Cyber Dranzer, which in return turned the poor guy into a maniac after letting the bit-beast feed on his energy. Once he finished the battle, he starts going insane and crumbles down to the ground and actually dies after Cyber Dranzer was too strong for him to handle (he goes mentally insane in the English dub, which is also pretty heavy). He rests in Kai's arms, leaving Kai regretful for how he treated him whilst Team Psykick leaves him to die. You can't help but feel sorry for the poor guy...
Mathilda. She's shy, timid and quiet as well as being forced to follow the strict rules from her coach, Barthez (which included destroying her own bey for the sake of winning). She is genuinely terrified of her coach since he treats his team very poorly and tends to unleash a lot of his anger on them (as opposed to how the public think of the guy as a saint). In the Japanese version, it's even worse. Barthez physically abuses Mathilda too by pushing her against the wall after trying to stop him from hurting one of her teammates, Miguel.
Daichi. Say what you will about him but his backstory in the movie where his father dies after a construction accident and encourages Daichi to become the best blader is very heart-breaking.