Since when do people have a choice? Instead of "don't do dull work" (which might translate to "don't do what you are asked to do"), I say you do the stuff you hate as fast as possible. Engage it with zeal, and get it the heck over with as soon as possible.
If you avoid doing stuff you hate, the cloud of having to do it lingers over you; you are not really avoiding it, you are prolonging it. Just get it over with and move on. You'll deliver it on time (or earlier), and will have gotten past the hurdle.
We often have more choice than you might think. Here's an example - today my boss wanted me to write up a C header file - essentially I had to take an interface supplied to us by a partner, and modify it so that it respected our coding standards. Now, I could have spent 4 hours of hand-editting this (rather large) file, or, I could spend 4 hours writing a custom pretty_print in Ruby to do it for me. One way of doing it is very boring, the other is rather interesting.
More generally, boring = automatable. If the code that you are writing, or the other task you are doing is boring, it is ripe for automating - so automate it! You'll never have to do the boring task again.
I agree with you on this one. If dull work must be done, you have to do it as fast as possible and get over it. Otherwise you keep thinking on it while doing normal stuff, so you never get to rest and you are probably wasting time with other stuff (just so you don't have to do what must be done)
I like your do-the-dull-stuff-first philosophy. But you can't discount the fact that we stay in dull, drab workplaces as a matter of choice.
If you hate your work we each have the choice to go somewhere else. Be an electrician, or a garbage collector. Move to a different company that offers more compelling work, or start one that does!
I'm just saying we do have the choice to do work we enjoy, even if it means we sacrifice some security to drop the status quo and never look back.
If you avoid doing stuff you hate, the cloud of having to do it lingers over you; you are not really avoiding it, you are prolonging it. Just get it over with and move on. You'll deliver it on time (or earlier), and will have gotten past the hurdle.