Sensei's talk of the Amuro and Char rivalry made me giddy, but he did get a few things wrong. To review...
Lt. Commander Char Aznable attacked Amuro's home colony in search of the Federation's new MS. Amuro used the Gundam to destroy two Zaku MS and then he helped guide the White Base out of the colony port and there he and Char faced off for the first time. The 'rivalry' was really just a pride-wounded Char trying to hunt down the White Base and beat the 'White MS' because, well, he was prideful of his piloting, I believe. It wasn't until the third movie/late into the TV series where Amuro accidently stabbed Lalah Sune when she moved her Elmeth Mobile Armor in the way of the RX-78-2 Gundam's beam saber. From there on Amuro hated Char for puttin' Lalah in the middle of the war (well, more like the end of the war) and so Amuro blames Char for her death whiel Char just blames Amuro for actually killin' her. Seven years later Char--incognito as Quatro Bajeena--meets with Amuro on Earth as he and Zeta Gundam's protagonist, Kamille Bidan, try to return to space after the AEUG (Julian-sensei, pronounce it ay-oog!!

) dropped from space to attack the Titans HQ, Jaburo. Char tells Amuro that he came to Earth to laugh at Amuro because he hides from the new war because of his fear of space. Char believes Amuro fear space not because of the weightlessness that Amuro claims to fear, but because he fears seeing Lalah's spirit. After reclaiming his mojo, Amuro pilots for the Earth AEUG division Karaba in a Dijeh MS based heavily on the AEUG's Rick Dias, which is based on the Principality of Zeon's Rick Dom, a space model based on the Dom unit that Zeon fielded during the One Year War (OYW), most notably pilot by the Zeon ace pilots the Black Tri-Stars, best known for capturing (then Lt. General) General Revil in the early parts of the OYW. Anywho, Char and Kamille return to Earth again during an attack on Kilimanjaro and Amuro and Char must painfully watch on as they see Kamille mourn over the death of his version of Lalah Sune, Four Marasume a Cyber-Newtype (normal people or regular Newtypes who are genetically altered to be artificial Newtypes) when Kamille's rival, Lt. Jerid Messa of the Titans, kills her, his own comrade. Jerk.
About another 6-7 years later, Char returns to the Earth sphere *ell-bent on dropping Axis, a large asteroid once used as the remnants of Zeon's base, onto Earth. Here, Amuro and his Nu Gundam (Nu as in the Greek symbol) face off against Char's Sazabi MS. After a fierce battle
Amuro wins, and with Char's escape pod in hand, he attempts to use the Nu Gundam to push back a falling Axis from sending the Earth into a nuclear winter. With the help of the Federation's GM III MS, Londo Bell's Jegan, and oddly enough Neo Zeon II's Gara Doga MS, Amuro's Nu Gundam's Pscho Frame collects enough will power from all the pilots and Earth is saved from Axis. The Explosion of the Psycho Frame kills Amuro and Char at last ending a 13 year rivalry between the two and the Zeon and Federation.
Mr. Mike, if you wish to jump onto the Gundam bandwagon, I suggest starting with the movies MSG The Movie I, MSG The Movie II: Soldiers of Sorrow, and Movie III Encounters in Space. Sadly only subbed versions are available these days as the original dub (starring Michael Lindsey and Steven Jay Blum in the two starring roles) is harder then heck to find.
On the subject of the Podcast, fun episode, I loved it. WHEEEEEEEEEEEEEE!!!!!!!!!!!!!