These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Americans Hate Tingle: Lynn Minmay, because of Character Exaggeration/Flanderization in the Robotech dub, the fact that Reba West/Rebecca Forstadt, the actress hired to play Minmay was not up to the task, and that the songs written for her were likewise poor (especially the jingoistic "We Will Win," in the climactic battle, the total polar opposite of the original "Ai wa Nagareru", a very pacifist song.)
The whole Do You Remember Love? sequence, for the music and for being pretty much a Crowning Moment in anime history.
Crowning Moment of Funny: Hikaru calls Misa an Obasan in his first meeting with her (over the radio). Later, after he signs up with the military, he meets her in person with the sudden realization that she's now his superior officer. Cue an Oh Crap and Hilarity Ensues.
Fridge Brilliance: Bodolza attacks Earth when Zentraedi start defecting. Macross 7 makes it much clearer why: what was happening in the Sol system had every indication of a Protodevlin infestation.
God Mode Sue: Max, though it doesn't hurt his popularity any.
Also Canon Sue, though again, doesn't really hurt his popularity.
Holy Shit Quotient: Many, but the ones who stand up the most are the titular ship punching an enemy ship in the face (this even in-universe: after seeing it, Breetai and Exedore are left speechless for a moment before monotoning they need reinforcements) and Bodolza glassing Earth as soon as he's in orbit (a first in anime history, and lampshaded by Misa crying they can't do it as soon as she sees the data).
Nightmare Fuel: What, no one here who got to watch this show as a kid wasn't traumatized by the part where the whole Zentraedi fleet just pops up out of nowhere and immediately showers the Earth with their ships' cannons before the defense forces even gets to put up a fight? And that particular scene depicting a soldier's gallant but futile attempt to shield a little girl from the global destruction....
If anything, the creators acknowledge it: as per Word Of God, in the timeframe of Macross 7, Kaifun is part of the Macross 11 fleet where he manages an American knockoff of Fire Bomber, all while claiming they're the originals and Basara is the ripoff. Take That, Scrappy! or what?!
Strangled by the Red String: While the show foreshadows it before they've met, Max's feelings for Milia go from "let's go for coffee" to "be my soul mate" at the drop of a hat ( or a dagger in this case.). This is especially funny considering he declares his love right after she tries to kill him in a knife fight for defeating her, once in battle and then at the arcade.
Hikaru: Excuse me, but didn't you just go out on a date with this girl? I mean fun's fun, but jumping straight into marriage?
Tear Jerker: Roy Focker's death, especially when they show Claudia's reaction.
Not to diminish anything, but Focker's actions leading up to that scene may also qualify him for What an Idiot. YMMV, of course.
Actually, a bit of Fridge Brilliance could potentially fix it. It's not unlikely that Roy realized he would eventually die of the injuries he had sustained, or at least he considered the possibility. Therefore, Roy might have deliberarely chosen to take a risk and attempt seeing Claudia before he died, rather than kicking it all alone in the hospital. At least it offers a possible Alternate Character Interpretation... hm.