Regarding the branzino reference, you aren't the only one who noticed. This article in Vulture picked up the reference, too:
How could you forget this pivotal scene (assuming you did),
considering its inclusion in a post on this very website titled “The
Things We Can’t Forget From This Summer’s Movies”? Or that another
website, the Awl, asked you nicely not to: “Let Us Never Forget the
‘Spiderman’ Branzino Moment.” (Itself a reference to a blurb written
in the New York Times Magazine praising the fish as having the “Cameo
of the Year.”) By featuring one iconic close-up and what seemed like
16 separate references to the European sea bass, the branzino scene
from The Amazing Spider-Man was the fish-centric dinner scene from a
major motion picture released in summer 2012.
Thankfully, the most unlikely part of The Amazing Spider-Man resulted
in the most unlikely reference in a film lousy with references to
various bits and pieces of the Spider-Man universe. No one likes
spoiled fish — except that creep Heathcliff — so I won’t give too much
away about when the reference happens, but just know that spoiled fish
is a little hint, as one character is served branzino offscreen and is
not pleased with the result. (Once you get to know the character,
you’ll know the moment is classic that character.) Seems small, sure,
but this joke gets nearly as much screen time as Zendaya.
As for whether the line is a specific jab at the previous movie is up to interpretation. As Screen Rant said in this article:
Once Peter finally arrives at the Homecoming dance, he's barely given a moment to take in the surrounding before running off to save the day. But there's enough time to overhear Flash arriving, claiming that the dinner he just came from was underwhelming at best since "that branzino wasn't fresh." And he knows branzino. Which means he wouldn't have missed the sea bass being served at the Stacy family's dinner in Amazing Spider-Man. Whether Flash is implying that the fish was past its prime, or the film in which it appeared... fans can decide for themselves.