First things first, if you have not yet read and implemented parts of David Allen's 2002 book Getting Things Done, I highly recommend that you give it a try. No one can implement it all, but there are useful things anyone who needs to... well, get things done... can use.
I don't have a problem getting Things done. But getting Shit done is another story. Things are the core of our life... make that film, write this book, get that degree, raise this child, travel to that country, manage this project. Shit (often referred to in eastern philosophies as The Ten Thousand Things) is everything else that is collateral and ancillary to Things. Arrange for burritos at the retreat, take care of the image permissions for this paper, keep in touch with potential candidates for this program, figure out what the hell has that person's knickers in a knot, pick up eggs.
Things and Shit. Shit and Things. Even if you are fortunate enough to have your own staff assigned to managing Shit, that doesn't get rid of it. Human staff assistance is merely another technology, it might shift some of the Shit from your attention so that you can focus on Things, but for the most part it will just increase the amount of Shit you yourself can handle. You still have to have a strategy and method to dispense with Shit.
For several years now, I've used OmniFocus as my technology to handle both Things and Shit. The desktop version 1 was very good, synced perfectly to my iPhone version, and t served as a trusted, universal capture and inbox. Two problems: it's too complex and it's too expensive for me to recommend to students, who are the people who most need help learning to get Things and Shit done.
Right now, there's a program called Things (I know) that has been reduced to free for the iPhone and iPad (update: no longer free, but still pretty cheap), and if you're a student or a noob, you should get them right now. They sync to a desktop version that is also on sale for $40, but don't bother with that now. If you're using the stock reminders in your device, it doesn't have enough granularity or heirarchical structure to be able to meaningfully differentiate between Things and Shit. I'm liking the things app a lot, and given that the new desktop version of OmniFocus is truly terrible, I'm pretty sure I'm going to be switching everything over soon (update: I still use OmniFocus because my projects were a bit more than could be handled with Things, but I went back to v.1, because v.2 is still a complete abomination).
Go forth. Get Things done. Get Shit done.
Perhaps I should write the book Getting Shit Done. Then I can go on the a lecture tour talking Shit to CEOs. I'm putting that on my list.