My prot paladin is an alt for me, but I've been running a lot of heroics lately, and tanked a fair bit in TBC and Classic on my druid.
Practice will help with the constant looking at your action bars, and perhaps moving them further up your screen (or getting a cooldown monitoring addon) will help you monitor cooldowns without moving your eyes too far from the action. But ultimately, practice and getting the muscle memory working for you will be the biggest help.
When mobs run to somebody else, I'll generally taunt it back and hit it with something; maybe even making it my main target. However, with the current level of DPS and threat gen out there thanks to all the fairly easily attainable gear, nine times out of ten the mob will almost be dead anyway; it might not be worth taunting. One thing you could consider, is using a mouseover macro for your single-target taunt, so you can maintain your current target and still taunt. Personally, I just switch, and then give it a smack with some ability when it gets back into melee, and my threat solidly re-established.
For the camera, I also have it sitting about half way out, unless the boss is particularly large and I need to zoom out further to see anything other than it's bootstraps. This was particularly true in my pre-wrath tanking experiences as visibility was hard to come by as a main tank in a LOT of boss encounters.
For movement, I use a combination of the keyboard and mouse. Mouse for turning, and auto-run; keyboard for strafing and fine tuning of positioning. Positioning is something I continue to struggle with at times, as mobs just don't want to cooperate at times. I'm still getting used to taking avenger shield's daze in to account when pulling, as well.
In heroics, I rarely use 9696. For trash, I'll generally go in tossing a shield, simultaneously taunting one target, and from then on, focus mostly on aoe abilities. I'll also tab through the collected mobs for single target abilities if DPS are targeting different ones, or there's some strong aoe going on. If the DPS is fairly strong, a good portion of the pulls will die before anything approaching a rotation can be completed; so I'll often focus on getting snap-aggro on as many targets as possible. How I'll handle pulls does depend on the group, though. One thing I do find helpful, is pre-buffing a bit before pulls (sacred shield, divine plea, and sometimes holy shield), as I've had occasions where a GCD from holy shield on the way INTO melee range will cost me initial aggro, for lack of dps waiting half a second before starting.
Which leads to your next question. Some DPS will assist you, but most won't, and often tanks will change targets enough that it isn't even helpful to DPS. Don't be afraid to mark though. In most cases it isn't really necessary, our aoe threat is very strong and most people seem to have a solid idea of what to kill first (most dangerous mob > caster > quick kill > whatever else). I usually only mark in two situations: If there is a mob that is still quite dangerous, despite most people outgearing heroics these days, I will mark them to make sure DPS is on the same page. I will also mark if there is a particularly well geared dps that pushes really high TPS (in my experience so far, this is usually plate dps). Generally, they won't mind, as more often than not, they are in a raiding guild, know they are geared to the teeth, and often have to watch omen even in raids. Sometimes, they'll even ask for it, not wanting to make your job harder.
For threat addons... I have omen, but lately I've stopped using it. My main is a healer, so by and large I don't need it when raiding, and in heroics I really haven't found it all that useful. Most of the aggro loss in a heroic is simply because someone used a strong aoe ability early (bladestorm 2 seconds after the pull comes to mind), or DPS is targeting different things and their DPS is high enough that your aoe threat spam just isn't quite enough. In which case I might start marking (I have a macro to put a skull over my target, for easy marking). The threat mod I've been using lately is LDB_Threat (libDataBroker). It uses a data broker display add-on (fortress.. statblockcore.. etc...) to output blizzard's built in threat data. I have it set to a little box, right above my character's bar (middle of the screen-ish) for easy access. It tells me the name of the person next to me on threat, and a threat percentage. It also colours the text based: red means you have a solid aggro lead, and you're fine. Yellow means they are getting close, and you need to watch out. And green is you've lost it. Our main tanks prefer omen for raiding though, as it gives them more information (TPS, more than one person, visual indicator (rather than numerical) of just how close the other person is to their threat, etc...).
Just some general suggestions, some that have been mentioned already:
If you use clique / healbot / whatever when healing, I would definitely also set it up for prot. I current bind a handful of spells to a mouseclick over my unit frames: Hand of Protection, Righteous Defense, Hand of Salvation, Hand of Sacrifice, Hand of Freedom and Cleanse. I think that's everything for my prot set up. For the sake of muscle memory, I would try to double up as much as possible from your healing spec. In my case only Cleanse doubles up with Cleanse Spirit from my main. But along with FoL, they all share the same button set up as with my ret-offspec (PvP mostly). Being able to use the Hands, RD, and Cleanse quickly, and without having to change targets is immensely helpful.
A smaller tip you likely already know, but just in case: In situations where there is a lot of AoE damage going on, try to time Divine Sacrifice to be used alongside Divine Protection to help out your healer; maybe even Hand of Sacrifice you healer so they can focus on others without worrying too much about themselves. A prime example is phase 3 of the Black Knight in H-ToC.
Keybindings: Maintaining mobility, and accessibility of key abilities is important. You also want to reduce the chances of pressing the wrong ability. Part of that is just muscle memory, and part of it is reducing how far your fingers need to move (easier to maintain a correct idea of button location in relation to your fingers, without looking). I personally use a combination of the mousewheel (thanks to a very helpful post on these boards) and the buttons surrounding my movement keys. For me, the fact that I pvp plays a very big part in my keybinding selections, but I also feel that it is helpful in PvE. Everyone has their personal preferences, but I would definitely suggest giving mouse-wheel bindings a shot to see if you like it (UP, Down, and Click; multiplied by however modifier keys you use), it frees up a lot of buttons, and it's suprising how much it helped me with mis-presses and reaction times on abilities that were placed further away from my "rest position" at the movement keys.
Honestly though, it sounds like you've pretty much got a handle on the spec, and what you're doing, and I think what you need most is simply practice. Getting actions and reactions to become second nature, and having personal past experience to draw upon to help make snap decisions when the unexpected happens. As a healer, you'll already have experience playing a reactionary and pro-active game, so it's just a matter of getting some practice with your tanking ******** and translating those skills over to this other role.
And lastly, a parting thought: Think about what you like your tanks doing as a healer, and try to incorporate that into your own tanking style.