Nothing happens. I've had to resort to using my bow exclusively because using a melee weapon is too unreliable.

I've tried multiple controllers and have this issue with every one of them. It's like the game doesn't recognize the button press at all.

yeah, i've had the same issue on occasion. i think it may be something do with the loss of framerate during combat, quite often the controls become unresponsive when the frames begin to drop. not much you can do about it, and i doubt that any patch is going to improve the regular performance of the game. i am praying though that the whole slideshow freezing is fixed, and also the weapon drawing delays. we'll find out by the 2nd.

Ya.. My weapons swing perfectly fine when it turns into a laggfest but then if I try to open my pocket it doesn't open..

I've had this happen to me numerous times. I just sheathed my weapon and unsheathed it again and it would usually work.

I've noticed i have to press L1 sometimes 2 or 3 times to get a spell to cast.

I had the same problem...and i done it like you.....and it works..... (CONFIRMED)

Why the second?

this has happened to me, however what also happens sometimes it seems like my controller becomes unresponsive like the game stops responding, it fixes itself in a few seconds and happens only sometimes but is annoying makes me think my game is frozen.

This has occurred to me once so far. A quick re-load of the save file and presto, fixed.

Recently my shouts have sometimes become unresponsive during the heat of battle. Which is nice, as you can imagine.

This.
Usually they just don't work, and have to try it again in the next battle/some time later.
Ocassionally it'll happen 7 or 8 seconds after, which is just wonderful during some battles, most notably the Storm Cloak missions when I kill 6 Storm Cloaks with my fire breathing rather than attacking the enemy.