I killed the Legion at Nelson outside this quest, I am unable to complete the quest. All Major Polatli does is thank me but no quest dialogue is given in his menu to finish the quest. I found on here, http://fallout.wikia.com/wiki/Restoring_Hope that this is a bug, but I would like to know if there is any way around it on the PS3. Or am I required to completely start over the game, being penalized for exploring the game world? I can hardly play the game anymore thinking about it, what else will I come across in the game world and potential break the game because of the obvious bugs they put into it? Maybe the should just make "levels" like Fable if this is what happens when you give them a sand box to make there game in.

Well the point of the quest really is to make Hope strong enough to attack Nelson, so its kinda redundant. Just do the quest on your second play through and skip it on this one. It will be something to look forward to then.

Does he give any other quests after this one, or is this quest required to be finished to do any other quests. Maybe some Nelson quests possibly?

No, No and No.
You've missed one quest, it has several components but its one quest.

Alright thanks, I was thinking this was part of the main quest and thought I just destroyed my game.