Dynomutt is much more of a Hypercompetent Sidekick in this feature, in comparison to his Idiot Hero role in the original cartoon. Out-of-universe, having two goofy talking dogs in the same movie would be redundant. In-universe, Blue Falcon would obviously upgrade him over the years as technology improves to clear out the kinks, taking away the malfunctions and stupidity and program professionalism and efficiency into his sidekick.
He's also likely been doing the hero gig for long enough to mature, develop, and hone his skills.
At the start of the film, Simon Cowell ends up driving off Scooby and Shaggy trying to invest in Mystery Inc. This leads to the initial capture attempt at the bowling alley they hang out near. Later at the very end, Dick Dastardly is shown to specifically have a Simon Cowell mask after proving himself a master of disguise multiple times. Since he's been tailing Scooby for a long while through his vet papers, and always needs to twist the knife when he sees an opportunity to be evil, it stands to reason that Simon wasn't just a one-off cameo; he was Cast as a Mask the entire time and was a part of Dick intentionally trying to drive Scooby and Shaggy to a place he knew they'd be at for his Rottens to scoop them up.
At a meta level, Simon Cowell loves dogs so it would make sense for Dick Dastardly to have Simon Cowell as part of his disguise because as dastardly Dick is, he does care for Muttley.
For most of the film, it’s unknown just how Muttley got trapped in the Underworld. Then the whole “attached to their dog” thing comes up in the climax, and it all makes sense.
When the trailers revealed the introduction of the Blue Falcon, he was jarringly shown being "hip" with dabbing and being a modern-day goofball. The film then justifies this by revealing that this is not BF himself, but his son Brian who inherited the role after his retirement, so naturally he would be more pop-culture savvy than his dad and seemingly less fitting for the role as he seems to have slacked off instead of training to take over for his dad.
This also ties into Dynomutt's new personality and levelheadedness where knowing his son would have difficulty adjusting to his newfound superhero role, BF and Dyno agreed to have his body and software upgraded to where he would be smarter and more vigilant so that he could mentor clumsy Brian when BF isn't around because you can't have two goofball superheroes where the blind would be leading the blind.
Of course Dick Dastardly Took a Level in Badass. His partner in crime was gone, and counting on Dastardly to step up his game in order to get him back.
This can apply to the other two dogs in the main cast. Scooby needs Shaggy to get over his insecurity over being "unimportant" and grow a pair. Dynomutt needs Brian to quit showing off and get his head into the role as the new Blue Falcon.
It makes sense for the mystery gang to be voiced by new people. The gang in this film are much younger than the ones in the 2D animated movies.
When Dee Dee and Dynomutt are having trouble tracking down the last skull of Cerberus, Scooby takes over with his nose, and quickly picks up the scent. Great Danes were originally bred as hunting dogs, and so Scooby is naturally equipped for tracking quarry the old-fashioned way.
Dynomutt is bitter at his former master's retirement, and slow to accept Brian as a new partner. He also gets a lot of scenes where he leaps into action to protect his allies, cementing his role as the team's guardian. Dynomutt is a robot Dobermann, which is a guard-dog breed known for their intense loyalty.
Daphne dressing as Wonder Woman in the prologue is both a continuity nod to all the times the franchise has crossed over with DC comics, but also foreshadows the climax: Cerberus is a monster from Greek Mythology, the type Wonder Woman frequently fights due to her own Greek roots.
The film subtly nods to the tradition of Scooby saying his name at the end of a Mystery Inc. caper. While he doesn't do this at the end of their first caper nor immediately after Dastardly is defeated and hauled off, he does get the last line: "Let's Scooby-Dooby-Doo it," said during the Dance Party Ending.
