Hi there folks, been playing Skyrim since launch. Great game, aside from a few minor issues.

-Walking/running problem-
I like to hold down the shift key whenever I run, so I changed the default mode from walk to run.
However, every so often, my character will walk instead of running and vice versa.
This can quickly get very tiresome, especially in combat situations.
It usually happens right after I enter/exit a new zone, check my inventory, check my map, etc.
I couldn't find anything on Google nor the forums, so I guess this isn't a widespread problem...

-3rd person camera rotation-
Every so often, I fail to best my enemy and have to make a quick getaway.
Back in Morrowind and Oblivion it was extremely handy to able to rotate the camera so I could see what was going on behind my character.
However, in Skyrim, this seems to no longer be possible. I can't even look at my character unless I unequip my weapons and stand perfectly still.
Is there any way to circumvent this?

Hope I'm not being to demanding. I can live without the camera thing even if it feels like a regression,
but It would've been kinda nice to be able to play the game without having to hit the toggle button every other minute.

I would suggest getting a controller but you probably don't like that idea ._. I can look behind me while running forwards in the 3rd person, and all that other stuff. Hats off to people playing this game with keyboards, I could never play well using that.

However you'd think the mouse would act as some kind of puesdo half-free flying camera.

To the first one, sounds like your cap lock is getting turned on. It's the walk/run toggle. And since it's next to shift, easy to catch in error.

Also note that if you press caps lock in a menu, it won't toggle and when you exit back to gameplay, it's function will be reversed. (Off walk and on run)

I thought so too at first, that's why I reassigned the toggle to the '?' key (it's close to the return key, so it's rather difficult to accidentally press; should probably have mentioned that in the OP).
Alas, nothing changed.

So, nobody but me have this problem? That's just my luck

For the first, yes - that does happen if you have your finger on the toggle when something changes - like a dialogue starting - it will then be reversed. It was the same in Oblivion.
I believe you can set the toggle somewhere so it's always on walk and you have to hold it to run but I can't think where that setting is offhand...
In skyrim you cannot rotate around your character like you can in Oblivion.

I have set the toggle to a different key so I won't accidentally press it when I play.
I never had this problem in Oblivion, ever.