I would ask that tanks try to avoid having tunnel vision.

Having good awareness of the monsters, their actions, and your party are important to both tanks and healers. Paying attention to status effects and the environment are also pluses.

When I tank and stop after a pull, I often swing the camera around so I can see what is going on behind me. That way I can spot any stray monsters and pull them back quickly.

I also keep an eye on the party list, constantly watching the healer's MP as well as HP of all party members. If I see someone's HP going down, it tells me I am missing something so I try to find and correct it.

Also make sure all the mobs are finished off before running to the next patch, and keep an eye on the whole party to gauge if people are ready for the next pull.

There is a lot going on and it's hard to keep an eye on everything at times... but I think good awareness is an important skill for tanks to have.