My first thoughts were how complicated the tanking rotation was in comparison to a bear. Bears have a rage bar and some cooldowns to watch while tanking. Death knights have that plus 6 runes of 3/4 different types all on their own cooldowns. For someone new to tanking on a death knight it takes a bit of experimenting to figure out which combinations of abilities can be used sequentially.
For me it mostly seemed a trade off between death and decay and spreading diseases with pestilence. Can't do both without waiting for runes to become available. So it's a trade off depending on the pull. The main deciding factor for me was asking myself if my target would live long enough for me to put on my diseases and spread them; if not then death and decay.
The other thing that I noticed was a lot of a death knights mitigation abilities also use runes, the same runes being used to build and maintain threat. That was a foreign concept to me as a bear where I can blow barkskin or survival instincts whenever I want provided they are not on cooldown. This requires a death knight to keep tabs on runes so that emergency mitigation abilities can be activated as soon as they are needed. Worst case scenario otherwise is a 6 second wait which may or may not be survivable.
I'm sure some of this if not all of it becomes second nature to a death knight tank with practice. I know when I first started my death knight I spent more time looking at cooldowns than I did my surroundings. Good thing death knights can survive an add or two or three without blinking. I am now to the point where I can DPS with minimal rune watching. I was also tanking with a DPS focused blood spec which probably lacked some tanking talents which may simplify things.
The one major weakness in a death knight tank I noticed is what happens if someone pulls off of you in those crucial first few moments. A death knight stacks diseases on one target then spreads them to the rest so if something should get pulled off it won't get any diseases on it. Worst case scenario the mob getting the diseases stacked on it is pulled away and nothing else gets any diseases. Paladins have similar hardships recovering from losing aggro early in a fight as do warriors and bears to a lesser extent, but it seems especially annoying for death knights. Something to think about if you have a death knight tanking for you.