Executive Meddling: Numerous - the main brains behind the series were axed by the time the third game came out. The radically different Episode II was a result of this trope as well, which pretty much led to the series being reduced from six games to three. Ironically, the third game seems to be the most true to its spiritual predecessor and is generally regarded as the best in the series.
Franchise Killer: The series was meant to span six games (not counting spin offs)... Episode II sure fixed that.
Especially for European fans, as no one was gutsy enough to bring it over after the failure that was Episode II, both the game's fault and due to sloppy handling of the game's release in Europe; they did not release Episode I, unanimously declared to be a better game, and then they missed out on Episode III, which is arguably as good as if not better than Episode I.
No Budget: Episode III seemed to suffer from this. Full CG cutscenes were used only for action scenes, many actors were reused in the dubbing, some cutscenes have extensive slowdown and there were more than a few questionably translated lines. This game was also made during the time that Namco was being bought by and merged with Bandai, so money was likely spread more thin than usual.
The Other Darrin: The dub of Xenosaga The Animation was done by ADV Films in Texas, so no one kept the voices they had in-game. The Japanese dub of the entire collective franchise managed to keep pretty much everyone who was assigned to that character from the start. Richard Epcar, the voice of Ziggy through all three games, stated that he didn't even know there was an anime, or that it was being dubbed in Texas. Otherwise, he would have flown over there from California and auditioned for Ziggy.
What Could Have Been: The story was originally going to be very different for Xenosaga II and III before Executive Meddling caused the scenario writer Soraya Saga to be dismissed and the original script by Takahashi to be discarded. A portion of the old script was retained for the Pied Piper cellphone game. Among some of the things that were originally planned to happen for Episode II:
Citrine would reunite with her URTV siblings.
Shion's past history with Febronia.
Junior rapidly growing to an adult with both options available during battle.
The ghost of old Miltia.
The death of Sakura.
Brief reunion between the URTVS and grown-up Citrine.
Gaignun vs the Zohar emulators.
Junior and Albedo vs U-DO vs KOS-MOS 3rd armament.
Shion's spiritual seeking/witnessing/awakening.
The truth about KOS-MOS (removed)
Conversation between chaos and the Red Testament.
Conversation between Nephilim and Abel.
An antimatter annihilation of Albedo.
A grand majority of the series was eventually edited out. On top of the series originally being six titles long, the What Could Have Been page itself mentions that the series took up Chapters 2 and 5 of the original ideas, with Chapter 1 being the prologue scenes to Episode I. There's also a list on a Xenogears fan forum (spoilers beware) of things that could have been but were either put in later in the series or scrapped altogether when Soraya Saga left. For example, Jr. was supposed to grow up and have his adult form available in battle, as well as something called "Gaignun vs. the Zohar Emulators."
Several potentially awesome scenes were removed from the scripts of all three games, some being added in later, but not when they were originally supposed to be; and some were completely forgotten about. The most obvious example being the fight between Jin and Margulis, which was in the trailer for the original game but ended up being in Episode II. Another being a potential plot where KOS-MOS eventually got strong enough weapons to destroy a planet, which Shion was supposed to prevent. Also, chaos, the guy with the ability to destroy the universe, sits around and hangs in the background doing...well, not much. Just shopping and having cryptic conversations most of the time.