Yeah, DBM will give you the information you need for that kind of thing, although often you will need to know how to interpret the information. It also tends to tell you much more than you need to know (so you are more likely to miss a key piece of information), so it can be helpful to configure it for each boss, switching off the unimportant noise.
I find simpletauntannounce, or something similar, very useful, to tell me when the other tank has taunted.
For trash, threatplates is great: it magnifies the nameplates of mobs you don't have aggro on.
My favorite add-on at the moment is weakauras - it's not tank specific, but you can configure it for any class to give you lots of key information in a very visible (or audible) way. Theck on his Sacred Duty blog has some nice strings that will, for example, track eternal flame, helping you keep track of how powerful it is or will be.