The closest thing to an exception I know of is listening to music. I will listen to music while working on hard problems, but then I tend to choose music I know well and I use it to block out more distracting sounds rather than pay much attention to it.
I found I can listen to music so long as it doesn't have lyrics (non-lyrical vocals are OK). When I was in college, I had a special playlist of wordless electronica I would use for writing essays.
Someone once told me that there was a study showing that most music tends to decrease work effectiveness, but classic music actually increases it (I do not have a link). Sadly, I'm an uncultured boor and while classical music sounds pleasant it's not my favorite by a long shot. I compromised by including some techno remixes of classical compositions in my essay-writing playlist.
Maybe. In GTD, David Allen said that he met quite a few people who can only work effectively when they multitask. Some procrastinators only work well when they are avoiding another task ;) It's not great in general though.
Also, leaving one task lie while you mull over it can be good.
But I think making yourself feel snowed-under is bad, as is needless context-switching.
Having been a procrastinator, I know the feeling he's talking about. In fact, what I advocated above is basically large-scale procrastination of basic life activity like socializing.
And there's a difference between simply being able to work effectively and being able to solve a single difficult problem. For typical programming challenges that can be broken up into smaller chunks a bit of context-switching may not slow you down that much and you can be sure to give attention to important things like paying your rent and having dinner with your girlfriend.
Also, as a quick comment on your post above-- to the extent that "progress, even if it's not progress" isn't basically rephrasing my recommendations to study tools and similar problems, doing the 'work-on-context-instead' approach can be risky. If you spend too much time avoiding the big problem you may never solve it.
Music engages your creative hemisphere, thus hampering your creative thinking capabilities.
For me this wasn't a problem when configuring routers, but I found that if I listened to music, I could spend an hour programming a solution to a problem that could have been sidestepped entirely.
I read some articles about that, but don't have a reference handy. In any case, once I noticed the effects it has on me, I am being extra careful.
The closest thing to an exception I know of is listening to music. I will listen to music while working on hard problems, but then I tend to choose music I know well and I use it to block out more distracting sounds rather than pay much attention to it.