A Father to His Men - He is shown to care deeply about the people under his command.
Dirty Old Man - The bridge crew gets a few good snarks in as Global seems to be enjoying himself a little too much while judging the Miss Macross contest.
The Captain - Technically he is either (depending on the ambiguous Japanese term) a Brigadier General or a Rear Admiral.
Cool Big Sis - She acts like this often to Misa, commisserating with Misa over tea (or more alcoholic substances) later in the series, as the love triangle begins to close.
She wears Jheri Curls, for god's sake! Of course she's black!
On the other hand, the cast is pretty diverse, so it's hard to call her token minority. For the record, both Hikaru and Misa are Japanese, while Minmay and Kaifun are Chinese. It's just that Japanese artists traditionally do not distinguish between Asian and Caucasian features, so it's somewhat difficult to notice.
If anything she's an aversion - Japan has never had any social pressure for artificial racial diversity, and her being black has no real impact on the plot. If we had some race tropes equivalent of Straight Gay, that would probably apply.
Actual Pacifist - Subverted: In the episode Boobytrap, Hikaru calls Roy a murderer after Roy boasts of his kill tally, but a few moments later it's implied that this is him venting his anger over Roy breaking his promise to return to the air circus. Hikary soon joins the UN Spacy with what appear to be few moral qualms, mostly to impress Lynn Minmay.
Captain Crash - Has a tendency to trash his machines. This is even lampshaded in the episode Phantasm where even his own coma delirium mocks him for his repeated pancaking of vehicles.
Love Triangle - To the point that when Max asked him for an advice about Millia, he mused that he wished his romantic problems were so simple.
Otaku - While not one himself, his use of the over-polite honorific version of "you" early in the series is thought now to be the origin of the term.
The Other Darrin - Due to the death of his original seiyuu, Arihiro Hase, in 1996, in all subsequent appearances, he is voiced by Kenji Nojima.
Self Made Girl - In the TV series she starts as a waitress in her aunt and uncle's restaurant, then becomes the most famous singer in the world universe.
Ace Pilot - He's the best pilot in the show. This is acknowledged in games that have pilot stats; Max typically has high stats and occasionally special bonuses on top of it. In Macross Ace/Ultimate Frontier, Max (both younger and older version of him) has the highest (initial) stats out of any pilot in any Macross era except his "Vitality" stat.
Super Robot Wars Alpha Gaiden uses a different way to put this trope. Overall, Max stats is worse than Fokker, however he and Millia are the only Macross pilots that posess the Awakening seishin, signifying their ace pilot status.
Bunny-Ears Lawyer - Actually a toned-down Truth in Television version of this trope, particularly in the movie, where he actually shows up to rescue Hikaru and Minmay blind drunk and still proceeds to kick Zentraedi backside. In the TV show, Claudia mentions how once Roy shot down five enemy fighters with a raging hangover.
Badass: In the smackdown mentioned below, He destroyed a Valkyrie with his bare hands. Better yet, he also survived having said Transforming MechaBlow-up in his face.
Britai Can Breathe In Space - after being sucked out of his flagship into hard vacuum, Britai seems able to walk on the ship's exterior with no problems and re-enters the ship in time to lay a smackdown to Hikaru and the rest of the pilots.
Dark Skinned Redhead - Original incarnation-only (would later be retconned for the below)
My Brain Is Big - His DYRL incarnation (which became the basis for his subsequent appearences).
Justified in the later series by saying that he was suffering brain cancer from the repeated micro/macronization processes and so had to change his form drastically for some reason.
Shorter Means Smarter - One of the smaller Zentradi characters and serves as advisor/historian.
Bunny-Ears Lawyer: He may be called Ally Killer, he may be the Brute, his very first appearance on the show reveals he had bet on how many ships of Breetai's fleet he'd ram by folding out too near, but he's a very competent commander and a very good pilot.
Crazy Awesome: In the movie She uses a Zentradi for a shield, shoves the barrel of her weapon into one's face then pulls the trigger, rips one in half, stomps on the head of another and is able to give Max a run for his money.