Sazaki is often called Gyandere, due to his obsession with Sei and his preference of Gunpla.
Rinko is called Mama-n, the suffix ~n is used in Japan as to point out cuteness aloud.
Also it sounds the same like the Japanese slang Maman, who is the equivalent there of the phrase MILF.
The moment Sengoku Astray appear fully as model kit, it earned the title Weeaboo Astray, being overtly Japanophile all around (even the name Gundam is written in Kanji)
In certain Imageboards, the show also called "Gunpla/Gundam Boy Friends" due to abundance of shipping material, both the Ho Yay and straight variety.
Rainer Cziommer, due to his Wild E. Coyote tactic, is now know as "butt-hurt NTR guy" in Japan.
The alliance of pilots who attack Fellini in episode 11 was quickly dubbed "Team NTR", since their entire motivation was to exact revenge against Fellini for stealing their girlfriends (though he insists that they came on to him).
Aila's Qubeley Papillon is slowly getting the nickname "Uberley" for being overpowered against other Gunpla that it faces.
Nils Nielsen is now known as NiNiNi - for Ninja Nils Nielsen, which is what he becomes when he's not doing Gunpla fight.
As soon as the Renato brothers started to snark at Luang Dallara's defeat during the episode 17 stinger, the western fandom quickly named them "the evil Lockon twins".
Ditto also for Mobile Suit Gundam Wing: This series marks the reunion of the seiyuus of two of the Gundam Doctors (Doctor J and Master O), as Master Chinnan and Mr. Ral, respectively.
Screwed by the Lawyers: Due to various legal agreements with Japanese TV networks, Mobile Suits that have aired on MBS and TBS in the last 5 years cannot be shown in Build Fighters. This means that, while suits from season 1 of Mobile Suit Gundam 00 are present and represented, suits from season 2 are a no-show; same goes with Mobile Suit Gundam AGE.
Although given its OVA release nature, Mobile Suit Gundam Unicorn is apparently fair game, considering a Loto did show up in the series.