I picked up Skyrim yesterday and was beyond excited to play it, but I'm now starting to run into glitches that are making my game almost unplayable.

The first one was minor; a quiver of arrows I had sold to a merchant in Riverrun was somehow still stuck on my character and now matter what I did, no matter what armor I changed out of or into, it was still stuck on my character. To complicate things it wasn't in my inventory, I looked through twice and I did not have any arrows on my character, yet there it was.

Second, my world map completely inaccessible. I can not access it at all. This started after my first dragon fight.

Third, when NPC's give things to me, they do not always appear in my inventory.

Fourth, after coming out of dialogue or entering through a door my view will shift to the right and lock in that position, pushing my character to the left side of the screen. I cannot walk at the usual pace when this happens.

I love Skyrim and would like to resume playing, but it got to the point I had to restart my game. My 360 is less than a year old and in excellent condition. Memory still has room.
Any help would be much appreciated,