The Ace: Max. Downplayed since he's in charge of the battleship. But when he goes out to fight, he proves that he's still got his touch.
Ace Custom: The Sound Forces Valkyries are modified versions of existing fighters.
Ace Pilot : Max and Millia are former Aces from the original series. Gamlin is stated to be one, and Basara counts, in fact Max himself stated that Basara is pretty good, although not as good as himself in the past.
Artistic License - Linguistics: There is a suggestion that the words evil and devil originated in the Protoculture's conflict with the Protodeviln. However these words were derived from older languages in which the words sounded considerably different (devil started out as diabolous, for instance).
Attack of the 50-Foot Whatever: Some of the Protodeviln. In the movie, Emilia featured a somewhat funny side-effect of being giant-sized; namely, bigger body means louder voice. She couldn't sing in a populated area while full-sized without disrupting the peace.
Authority Equals Asskicking: Max and Milia. Max is the Macross 7 battlefleet commander, and Millia is the Mayor/President of Macross 7's civilian government. Justified Trope in that they were Ace Pilots before reaching their positions of authority.
Don't call Milia "oba-san" (while literally "grand-mother" in Japanese, the actual meaning can range from a respectable "Mrs." to "old lady" or even "old hag", although the latter would be probably better expressed by "baba"), or else, even when it is quite possibly literally true, since her and Max' first-born is 34 years already. Millia also looks quite young for her advanced age, presumably due to her being a meltrandi (female zentradi).
If Basara sings a song for you, listen to the end, or else. And also don't make him save you by using violence, which he absolutely abhors. And also, don't attack Mylene, while he is around, or else he'll kick your ass and then chew out Mylene for making him save her by using violence.
To the point that if someone attacks her, he'll break away from being an Actual Pacifist and punch whoever attacked her. Of course, afterwards he'll yell at her for having made him attack someone, showing how much he hates violence.
The movie (or in-universe movie) is about the events from the original Macross series, in which both Max & Milia served in, (their marriage being one of the other culture shocks); so, that wouldn't affect either interpretation.
A Destroid Monster shows up in the Festival. Milia's Red VF-1 shows up as well.
Sharon Apple's music is still frequently played on the radio.
During the tabloids episode, the reporter is listening to "Information High".
Some Lynn Minmei songs are still played/used, (notably "Do You Remember Love"" in the Strongest Women episode)
Cool Ship: (a rock-and-roll band is equipped with customized versions of the most advanced mecha available)
Cool Old Guy: (Max Jenius. Milia may also qualify. Meltlandi must age like fine wine.)
The director stated age is a state of mind, and Max is a Genius.
Description Cut: In one episode, Basara throws an apple to Mylene as she's heading out for a date with Gamlin. Mylene tells Basara that there's no way Gamlin would take a bite out of a whole apple. Cut to Gamlin taking a bite out of the aforementioned apple.
Determinator: Basara. As a kid, he'd sing songs to a mountain everyday in an effort to literally move it by singing alone. Even in a wind storm. While playing a guitar that was almost as big as he was.
Not to mention the fact that he absolutely refuses to let anything, and I mean anything, stop his singing. Someone's trying to punch him? He keeps singing. Someone is actually using him as a punching bag? He keeps singing. He gets ordered to do something else? He keeps singing.
Did You Just Teach Cthulhu To Sing: The Protodeviln eventually realize that singing allows them to produce their own internal Spiritia, and no longer need to steal human Spiritia.
Ditto Aliens: Averted: except for one matched set, no two Protodeviln even vaguely resemble each other)
Dying Moment of Awesome: Diamond Force's Commander Kinryu got one. The Battle 7 was in the middle of transforming when one of the Protodeviln ships was about to fire at it. Even though he was in a VF-11C, Kinryu had it purge its armor, charge into the Protodeviln ship, and fire at its core after he got inside in a Taking You with Me. Oh, and he did all this when by all rights, he should have been in a hospital bed. The scene can be seen here.
Kinryu: What is Diamond Force if I can't bring down one battleship?!... Here's your love heart!
Establishing Character Moment: Basara has three. The first one involves him singing at a bunch of thugs to make them stop fighting. The second (same scene) is when he gets mad at Mylene because him trying to protect her ended up making him attack the thugs. The third is him going out in his Valkyrie into a battlefield to try and stop it by singing.
Fangirl: While Fire Bomber gets to be pretty famous, the Flower Girl is definitely Basara's Number One fan. One episode focuses on another fan, though this one's a boy on Mylene. Also, the Fleet of the Strongest Women episode; must be seen to be believed.
Jerkass: It's hard to see why, if he weren't a Messianic Archetype, anyone would put up with Basara at all. He's continually blowing out the rest of the band, and, indeed, their fans, for his own reasons. He endangers the lives of military and civilian personnel by turning up in combat and getting in the way, and is completely insensitive to the feelings of pretty much everyone around him. This also ends up being one of the main criticisms non-Japanese fans, in particular, level at the show; he's such an unrepentant, unrelenting ass, and never really changes or gets called on it, that it badly stretches viewers' suspension of disbelief.
Karma Houdini: Despite repeated unprovoked attacks on the Earth Forces, kidnapping an entire colonization fleet, sucking the life force out of anyone whom he didn't kill, and nearly wiping out all life in the galaxy, Gepelnitch gets to fly away to live peacefully somewhere else... in the body of the dude he jacked before the series started.
This charge is also occasionally leveled at Basara; he is an unceasing jerk to nearly everyone around him, and never really gets called to the mat on it or made to change, and by the end it seems like his behavior's been completely vindicated.
Ki Attacks: ...through the power of rock and roll.
Loophole Abuse: In episode 6, Gamlin was out on patrol when he found a disguised enemy craft. He chased it for a little while, but it got away. When he asked for permission to search for it, he was told that it fell out of the range of his duties, and that he should let an investigative team search for it and enjoy the vacation time he would be getting the next day. His response was to say that his vacation time started in one hour, and that he wanted permission to continue searching in his free time. Needless to say, he got permission.
Oddly Named Sequel: This is not the seventh Macross series, but the number 7 is a recurring motif in it.
The Ojou: Mylene, although she subverts large parts of the trope; hilariously her "bodyguards" call her "ojou" even though Macross Seven is a democracy.
It's the fact that she is the daughter of a high-ranking official AND their boss' daughter. They do so out of politeness and their desire to keep their jobs.
One-Man Army: The Protodeviln. A single Protodeviln was able to take out an entire Zentrandi fleet. Remember the original series and how there were literally millions of battleships? That was one fleet. The feat was so impressive that Zentrans have an innate fear of Protodeviln built into them.
Parental Abandonment: Borderline with Mylene. While both of her parents are alive, they're also the commander of the fleet and mayor of the city and, for obvious reasons, extremely busy with work. One recurring bit in the story is her improving relationship with her parents.
Diabolus ex Machina stalks the Flower Girl, thwarting her every chance to give Basara her bouquet.
Also, Veffidas using just about everything like a drum.
Basara's frustration at the way the Protodeviln never stick around long enough for him to finish his songs.
Screw the Rules, I'm Doing What's Right: Gamlin does this in episode 32. The military has impounded Basara's Valkyrie, and the Protodeviln are curb-stomping the new Jamming Birds unit. Gamlin then proceeds to take his Valkyrie over to where Basara's Valkyrie was being kept and helps Basara take it out so he can save the day.
Sivil's outfit, with tight leather and what can only be described as stylized breast-baring.
Mylene's outfits are pretty bad too, but then again she's a female rock musician.
And even then, it's only her stage outfit that really Shows Some Leg and is rather skin-tight; her "everyday" outfits are perfectly sensible (and more jaded viewers/anime veterans would say "almost puritan", compared to what her successors and other characters like her wear today).
Star-Crossed Lovers: Sivil is into Basara. Basara appears to be into Sivil. But Sivil has very nearly killed him already, and it might happen again. Sivil leaves, Basara decides he'll travel the Galaxy too...
Stock Footage: One of the big criticisms of the show - many battles, particularly in the show's first half, have mostly the same recycled scenes in the same order. The second half gets somewhat better about this, but it's still there.
The big reason the show takes so much flak for this is that Macross 7's franchise - from its predecessor, to its contemporary, to itssuccessors - uses "lack of stock footage" as something of a point of pride. Even SDF Macross, for how small its budget was, was very good about obscuring its use of stock footage and making sure things felt fresh. M7's blatant footage reuse felt like something of a betrayal in comparison - not helped at all by the fact that it was literally airing in tandem with the release of Plus, and the inevitable comparisons.
Unfortunate Names: Ray and Lt. Kinryu's former elite fighter group. It doesn't matter how badass a fighter squadron you guys are, "Pink Peckers" is not a name calculated to strike fear into the hearts of your opponents.... or anything else, aside from gay/genitalia jokes....