Great list.

So, yeah, Terra, you got abducted as a child by Emperor Gestahl...yeah...and then when you were 18 they put a slave crown on your head...

What about the 17 years between those two events? What did they do with her? Does she know Celes? Do they have a history together? What about the REST of her memories? T_T I've always found this an irksome thing.
I can't believe I never thought about that, there's so much missing from the storyline. It would have also been good to give her a history with Celes, especially when their names may have been inspired by the same thing (using her Japanese verison name; "Tina")

Locke said he was going to protect Terra no matter what, then promptly leaves her with someone she's never met in a place she's never been and doesn't know her way around. I do not think "protection" means what he thinks it means.
I think Locke knew he could trust Edgar, I get what you mean, but I think he knew she was in safe hands.

Terra has green hair, and nobody cares. She is absolutely, I guarantee you, the only person in this entire world with green hair, and she walks through populated areas unquestioned.

This wouldn't be half as bad if she wasn't being hunted by the Empire at the time. Don't they want to protect her? Shouldn't she cover her hair to hide her identity or something?
This is kind of a cop out, but pretty much everything outside the game shows Terra as blonde, so maybe in canon she is supposed to be (though why they made her hair green in the game, I don't know). Another thing is maybe they wanted the character to stand out, so they made her hair green.

The fact they can't seem to decide on whether her hair is green or blonde (I'm going with green) is a headscratcher itself, but I agree it's a plothole that no one seems to care about her hair being green, for reasons you said.

Sabin has just revealed to everyone within a 5 mile radius that Vargas has killed his Sensei (Vargas' father), Duncan.

Edgar utterly drops the subject when the scene afterward plays. Not "I'm terribly sorry for your loss," but "We're going to the Returner Hideout, derp."

This guy took Sabin in when he was homeless and trained him for 10 years. Sabin later remarks that the dude's wife treated him like a son. And Edgar doesn't say boo about it. Cold chillin', Edgar.
The whole scene is lacking in the emotion, and is sadly rushed. Someone once pointed out that Sabin and Edgar's reunion itself should have been a more emotional time, but all we really get is Locke saying "The brothers are reunited!" and that's it. With both this, and Edgar's comforting of Sabin over Duncan's death, the only way to solve it to just assume it happened of screen at some point (oh look, another cop out).

Also, why bother having Vargas escape the battle instead of die if they're not going to even bother with him in at least one more encounter? Unless they gave him the "escape" animation by accident... I don't expect him to keep appearing, but maybe a World of Ruin rematch?