Xbox – No narrator voice during cutscenes in Borderlands on Xbox

You can only get experience for a mission once per playthrough. If you completed the mission by yourself and then replayed it in co-op, you would not get the experience a second time. If you complete a mission in co-op, it will count towards your single player game for all players involved, if they have not already completed it.

It is also possible that you are not eligible for the mission, which means you have not completed the prior main story-line missions and are not far enough ahead in the game to get that mission by yourself. You will not get the rewards when another player turns it in. If this is the case, it will say so next to the missions and will not track progress for the mission.

Edit

Well since people are actually reading this, there's a little bit more information on each point.

The answers in order:

• Yes - All quests reset - The game begins just as though you had started at lvl 1 (minus the character selection, so you'll have to do everything over again (including the tutorial!)
• No - You keep everything - This is pretty straightforward, what you have on you at the end of playthrough 1 stays with you. However, items in playthrough 2 are scaled (see below on scaling). So you'll find the same named weapons but they will have better stats, so don't just ignore them.
• Yes - Mobs scale to your level -It is expected that after completing your first playthrough you will be around lvl 35 (give or take). Therefore when you start a new game, the mobs will have 35 added to their level (again give or take a level). Which is why specific enemies (like Crawmerax for example) have a set level. If you're looking to do the Secret Armory of General Knoxx, you should be lvl 50ish (about 2.5 playthroughs).
• No - You can go find it in playthrough 2, or you can access playthrough one with your current character (so if you have gained a level in playthrough 2, that level sticks when going back to playthrough 1). This includes any subsequent playthroughs.

Hope that helps!