Season 2 makes a large deal out of Star's struggle to "dip down" to control her magic without her wand, which is tied heavily to her turbulent emotions and growing feelings for Marco. However, come the multi-part premier for Season 3, the "dip down" suddenly turns into a Literal Metaphor and Star inexplicably gains full control of her powers, with no resolution to her complicated relationship with Marco at the time.
The implications of the main characters being able to go anywhere in the universe at the drop of a hat via dimensional scissors are never addressed, and in fact the scissors get outright ignored whenever they'd provide a too-quick resolution to an episode's problem. Even if they get used for some other purposes in the same episode. This is particularly jarring in Season 3, which treats Earth and Mewni as if they're separated in some important way (with Marco for some reason thinking he has to either abandon Mewni or abandon Earth forever in "Sophomore Slump") even though travel from one planet to another is easier than walking across a room.
In "Star on Wheels", Marco has Star's wand. It's shown that whoever wants to wield the wand can have it change form. Marco could have tried to use the wand to save Star, but the idea never crosses his mind. The season 3 episode "Deep Dive" later addresses this scenario.
"Spider with a Top Hat" takes place inside Star's wand. At this point, Star is of course missing a piece of her wand, and it has been acting up throughout Season 2, but the episode does nothing to explore it. Instead, the episode immediately following it has Star going inside her wand and exploring the matter of her magic not working right.
According to the writers, Marco was on Mewni for weeks during the Battle for Mewni special, and hadn't told anyone where he was going beforehand. This could have led to him being confronted by his parents (who would have been worried sick) and Jackie, who would have been angered that he didn't tell her or be distrustful of Marco for secretly running away to find a girl who just confessed her feelings for him and then proceeding to stay with her for a duration. But we saw nothing of that. Likewise, it seems odd that they went through a big setup of having Marco abandon Earth in order to have him live on Mewni for the duration of Season 3, when there was already a long period of him living on Mewni off-screen between the special and the start of Season 3 proper.
Buff Frog becoming Mewni's new Monster Expert in "Starfari" ends up leading nowhere as, in his next appearance in "Is Another Mystery", he ends up leaving the kingdom with several other monsters. He does state that he was facing discrimination and was having trouble fitting in, but we never get to see that due to his absence in-between those episodes. He doesn't even appear in "Monster Bash", despite the plot revolving around an attempt in bridging Mewmans and monsters.
Season 3's episode "Deep Dive" had Marco use the Wand himself, it changing shape to a more monstrous design, and Marco temporarily gaining cheek marks of his own in the form of Crescent Moons. At the time, this created much speculation as only female members of the Butterfly family had exhibited cheek marks, and the design of Marco's version of the wand raised many questions due to prior forms of the wand reflecting their users. By the series finale however, the appearance of the wand is never explained, and Marco's cheek marks are written off as the result of exposure to magic.
The Magic High Commission being siblings and Glossaryck being their dad is information limited to the tie-in books, with the only time it's even remotely referenced in the show being "Meteora's Lesson".
Season 2 spent several episodes attempting to humanize the main members of the Magic High Commission,note Marco chasing after Hekapoo in the Neverzone for years and becoming close friends in the process, Omnitraxus trying to be a Reasonable Authority Figure to Star, and Rhombulus confiding in and forming a friendship with Star Season 3 however began depicting them as an Omniscient Council of Vagueness responsible for several crimes against the Butterfly Family and all of Mewni.note Allowing Shastacan to give Meteora up for adoption, replacing her with the piefolk Festivia and creating the False Dynasty, imprisoning Eclipsa and Globgor to prevent revealing the existence of the False Dynasty, doctoring the archives While this initially appears to be set up for them being a more morally grey group of characters that retain their humanizing traits, its ultimately wasted come Season 4. Season 4 turns them into Knight Templar characters willing to go to any extreme so long as they remain in power. Any humanizing traits they once had are gone, and the only one to have a Heel Realization, Hekapoo, only does so out of disgust for the others enjoying Mina's onslaught, and still decides to let Mewni burn while she takes Star, Marco, Moon, Eclipsa, and Meteora to the Tavern at the Edge of the Multiverse so she can wait till Mina's rampage blows over. Come the series end, the three are ultimately no more than a Big Bad Wannabe that end up dying with little fanfare.
In "Sleepover" Marco admits that he doesn't really know Jackie all that well aside from the pedestal he's put her on. You'd think this would lead to the show exploring Jackie's personality, family, etc. but nothing ever comes of it.
The Blood Moon plotline. Introduced in Season 1, it quickly captured the fandom's attention with the possible mystery and effect it had on Marco and Star, apparently binding them together in an apparent romantic attraction that was possibly unwanted and unnatural for them. To some fans, this came across as possibly, a very witty deconstruction of the cliche of male lead/female lead pairings in a lot of media, as in, a romantic pairing that the story has because it is a common trope, rather than because it makes sense for the characters. That said, the Blood Moon is mostly a background element that gets very little exploration up until the plot is solved in a late episode and Marco and Star still get together anyway, indicating that it didn't have much influence either way.
Despite Marco's parents housing and taking care of her daughter, Queen Moon never shares a single scene or conversation with them. In fact, the only time she's on Earth (not counting the first episode) is when it's to abruptly take her daughter back home in "Starcrushed". It would have been interesting to see how she'd react to them and technology on Earth.
King River doesn't have a conversation with them either, but he at least gets two episodes where he's on Earth and visits the Diaz's house. In fact, Marco's parents are noticeably absent during the majority of "Royal Pain" despite the entire episode taking place at their house. It's rather jarring that the two sets of parents never have a scene all together given the close bond their kids have with each other.
Counting Monster Arm, Marco's technically part-monster. It would have been interesting to see how the Mewman characters would have reacted to this news, particularly the King and Queen, who were housing him without this knowledge. However, Monster Arm is never brought up again after its debut episode, so this concept is never explored.
Even more egregiously, it was known that Star had a crush on Marco by this point, making her situation the exact same as Eclipsa's. Not only would this have given Star and Eclipsa something to bond with, it would have also given Mina and the MHC the perfect reason to turn against the duo. It also would have made Moon's actions in season 4 more believable, forcing her to choose between her people or protecting her daughter. Again, this concept is never explored.
