Well, I think they're cute. Your mileage may vary.
The theory behind The Monkey Business Illusion is that concentration on a specific set of tasks can often make us blind to tasks right in front of us.
This video explains this extremely well with the example they provide.
Now I'll give you a real world, business example from my own checkered past.
I was working for a game company in Washington state. We were making a forum/collaboration/blogging site for them. We had our eye on the prize: a demo for upper level executives by a specific date with specific features. That was basically the girls in white passing the ball to and from each other, despite the distraction of the girls in black doing the same, if you're comparing us to the video.
We also knew there was going to be a gorilla in the mix (as opposed to in the mist, which I could not pass up, I'm sorry). We had to have a demo of the software to the tech support department before the executives. We knew the gorilla was going to be there, and we figured we could manage it by using similar procedures to managing our current "white team ball in motion" strategy, and just, you know, keeping an eye out for the gorilla.
Which is probably why we missed an important piece of the puzzle: the effect the gorilla would have on our game in progress. In the video, which I've watched three times now, I never see the black player leave the game. Even though I know the curtain changes color, I still have trouble telling when it does (and after a few days I'd forgotten entirely and was wowed all over again). This is because I was watching the team in white pass the ball and the only thing I was looking for unusual was a gorilla.
In my real life business example, however, a player fell out of play (so to speak) and that changed the curtain colors for the executive preview. See, tech support doesn't look at a demo the way that executives do. They're pokey--for values of poking at things, rather than being slow. Tech support people are never slow. They should pokey--any poking they miss they'll have to deal with in terms of placating angry customers on the phone.
The gorilla came in and we saw it and we were happy; they saw the demo and played with it and only had one complaint...the ability to use improper words on the site had not yet been implemented. They learned this from entering every swear word they could think of into the demo space. You know, the demo space the executives used that afternoon. Notice the change of the curtain color? I didn't.
Our rep with the company we were working for was caught having to explain why "Mother F****ing Mother F**er" and other more elaborate and unpleasant posts were all over the demo site. I can only imagine him tap dancing there in front of them, explaining the filter would be done soon so this would never happen again. What I do know I saw was the thin smile on his somewhat red face when we talked about it; fortunately, he has an AWESOME sense of humor (and I'm not just saying that because he could be reading this) and we eventually burst into giggles. He had saved the day with the executive demo--we counted the correct number of passes, to extend the Monkey Business metaphor, but wow did we miss a few other things.
The moral of story is that there are always more parts in motion than you realize. Sometimes people outside of the equation will affect it, and sometimes you'll miss the monkey all on your own--after all, half the people who watch the video above for the first time miss the gorilla entirely.
This is why as a manager, good planning, good habits, and good people can help prevent you dropping the ball (or being mauled by a gorilla, or, you know, fired by executives offended by swear words).