The fact Carlos, the first of Tyson's opponents, has Kid Dragoon (or at least a custom including its distinctive Upper Dragoon attack ring with Kid Dragoon's colours) as the first known beyblade makes sense both competitively/meta and with the name. On the competitive and meta level, it shows he knows what he's doing but isn't a champion (that attack ring is part of a pair of rather useful customs, but even in the early plastic generation there were many better beyblades, both pre-packaged and customs), and overcoming him (through smarts and not force to boot) is Tyson's first step on the road to championship. On the name, it's Kid Dragoon, and defeating that beyblade means Tyson is growing up from kiddie level.
The tournament match between the All Stars and the Bladebreakers was rigged to assure that the American players and their gymmicks would have the advantage:
Steve vs. Tyson: a reproduction of New York streets. Apparently counterintuitive, given Steve's shtick is being a quarterback, and most usually see them charging... Thing is, a quarterback also has to dodge, and, as Steve points out when Tyson tries hiding among the buildings, it's easier with the unmoving buildings than with actual football players;
Eddy vs. Ray: a low gravity field provided by NASA. Again counterintuitive, what with Ray having Seen It All and Eddy being Basketball... Except it's about the gymmicks of Eddy's beyblade. Whose Flying Defense attack ring, thanks to its sheer size, gives it excellent equilibrium and near-impossibility to knock it out, and, with size and form, makes it fly. Not even Ray could find a way out of that...
Michael vs. Max: a baseball stadium, with the catcher place being toward Max's position. Given Michael's gimmick is being a pitcher, an obvious one, and a likely attempt to put pressure. It also symbolically foreshadows Max's victory: the place baseball's most popular is Japan.
Another piece of the American strategy for the match comes from analyzing the beyblades: Draciel is a defensive beyblade that would outlast the All Stars' attack-based beyblades (the only defensive one is Trypio, and that one's necessary for Ray and Driger), but Trygle's own gymmick is putting the wings of the base under the opponent's beyblade and jump (what it does all the time in the manga, in fact). The idea was to throw out Draciel if it somehow resisted the Cannonball Attack... And that's probably why Max angled Draciel to that it wouldn't get the attack ring under Trygle's wings.
The PPB is literally Backed by the Pentagon and the NASA, the beybladers have access to extremely advanced training equipment, and in the original Japanese version the President of the United States takes personal interest in the success of the American beyblade team. Ultimate Serious Business? Part that and part those beyblades hold weapons of mass destruction, it's only natural the US government takes care of them and the teens that can use them.
Before the match, the All Stars chalk up to luck the Bladenreakers' success in the tournament so far. Thing is, they're right: while the prediction of the Bladebreakers' defeat in the first match was clearly wrong, they should have been defeated 2-1 and knocked out of the tournament in the quarter finals, only winning due one of the funniest and most unexpected Ass Pulls in the history of anime (one that left the Bladenreakers themselves stunned speechless. Including the one who has literally Seen It All).
Kai's Badass Boast that no one can defeat his Dranzer G makes a lot of sense considering that, bar the match against Daichi in the world tournament, which Kai threw, no beyblader came even close to defeat Kai when he was using Dranzer G and when he did lose to Tyson in the finals, he already upgraded to the Dranzer GT.
One thing that seems odd in the third season was how Tyson/Takao freaked out over how his teammates all left. It could be Ho Yay, but think about his home life: his mom died, his dad is always away on work, and his brother left years earlier, and the only family that's constantly there for him is his loving, but slightly insane grandfather. To make a long story short, it wouldn't be surprising if Tyson has some abandonment issues.
During the BEGA arc, Boris shows off how powerful BEGA is by having his bladers, specifically Garland and Brooklyn, literally tear apart their competition. However, the only bladers that are tortured are Spencer, Bryan, Tala, and Kai, all bladers that used to work under him. He wasn't just showcasing BEGA's bladers, he was punishing his old subordinates.
When Tyson, Hilary, Chief, Max and Daichi can't find Hiro, Daichi looks under a rock. Seems just a throwaway gag... Except Hiro is a ninja. Is it that strange that The Ditz expects him to be hidden in places too small for that?