Most of the character dynamics, the basic plot and the sports theme of the first episode are lifted from tennis anime Aim for the Ace!. Coach in particular is an Expy of Coach Munakata. (Though really, this is almost a Bait-and-Switch, by the end.)
Likewise, Gunbuster's first launch is adapted from the pivotal battle of Getter Robo G, where the machine rises out the ocean, arms folded, and decimates the enemy's forces. Of course, virtually everyone on both sides of the Pacific now thinks of Gunbuster whenever that scene is homaged.
The final scene also homages Musashi ripping the reactor from his machine's chest at the end of Getter Robo.
Gunbuster is also shown launching missiles/lasers from all over its body in an identical fashion to Ideon.
Although never used in the show, an official card game showed Gunbuster using the Choudenji Yo-Yo and Choudenji Spin from Combattler V.
Hideaki Anno gave Gunbuster a single eye because he thought it was unique. However, he later decided it was a mistake because it didn't keep the robot recognizable when in shadows (Super Robot Wars, in particular, sometimes has to do a bit of "creative" lighting to get around this). This is why EVA-01 was drawn with two glowing, white eyes on a gloomy purple body.
Keep Circulating the Tapes: A drug scandal involving the OP singer, Noriko Sakai, kept it out of print for a while. These days it's out of print in Japan just due to its age, though the NA release is available if you look around a bit.
Playing Against Type: Norio Wakamoto as Coach Ohta. Wakamoto hadn't actually been typecast yet, as this was still earlier in his career, but Ohta doesn't have any of the VillainousLarge Ham that he has since become so known for. It helps that, naturally, he was also a lot younger when he played this role.
Science Marches On: In the show, the Solar System has several planets beyond the orbit of Pluto, including one that is called Jupiter 2. Sol is also part of a binary system, with the other star, Nemesis, being half a lightyear away.
Screwed by the Lawyers: This is perhaps why the OVA series has never been released overseas beyond the 1990s VHS and the 2007 DVD release, as it contains a "homage" that sounds extremely similar to the Chariots of Fire theme song. This got to the point where the 5.1x sound remix has it replaced.