Whenever I go to start a new game, I'll get to the character screen, but I won't be able to switch to body or head or any of the other tabs.
A similar thing happens if I go to set a map marker, It won't let me remove the current one, delete it, or even cancel out, making me have to close skyrim in order to keep playing. I do use mods, so if I need to I can list them.

Mods are often the most likely culprit, but if you're using the mouse, try disabling the 360 controller in the controls menu. I've read that there is some potential for conflict when it is left enabled, though I don't know specifically how this would manifest on the current version.

I also have an issue at times where my favorites stop allowing me to click them (or even work, in the case of Shouts). At some point though, I'm able to shout...does anyone know what causes this?It's really a pain when I can't even select potions from the Favorites menu because that usually means my death; the enemies I take on deal a lot of damage.

I've tried disabling the 360 controller option, so I guess it would have to be a mod somewhere. But what type of mods would I need to keep an eye out for while searching my lists?
Shademyth, do you have any mods enabled?

Disable all of your mods. If the problem doesn't persist, enable them a few at a time, depending on just how many you're using. This should help you narrow down the offending mod. Once you've identified the culprit, you should contact the author either through the Nexus or the Steam Workshop (wherever you got it from).

If the problem persists with all mods disabled, try starting a new game to see if it happens there too. If it does, then it isn't a mod. If it doesn't happen in a new game but does happen in an old game even with mods disabled, then you likely have a dirty save that has been affected by a mod. In this unfortunate situation you have few options, but I suspect this is not very likely.

Thank you, I will get started on disabling my mods right away.

I am back from disabling mods, and that didn't work.
What else could it be?

I have these mods:

Two-Handed Dawnbreaker
Non-Linear Perk Trees
Magic Font
Fur Hoods
Deacon's Frostier Frost
Sounds of Skyrim (removed)
Bethesda's HD textures (1 & 2)
Horse Armors (removed)
Bound Daedric Armor (removed)
Beast Follower Pack (removed)

**I play on PC , and I have disabled 360 Controller & Vibrate in Settings**

Be sure to list any "mods" that alter the code process or how the game is visually rendered. This includes script extenders, Skyboost, post-process injectors, etc. These mods aren't typically enabled or disabled - they need to be removed from the game directory to see if they are the source of the conflict.

I don't have any of those mods; I used to but quickly got rid of them when Bethesda released their HD res pack.