He mentions that re-writing a script from memory produces a better script. I discovered the very same thing in high school. The best essays I turned out where the ones were we had to write a rough draft at home, and type up a final draft due the next day, and I forgot the rough draft in my locker. I always attributed that to the fact that the first draft is an act of discovery, and inevitably carries cruft from wandering paths and dead ends. Starting anew is much better at removing the cruft than editing the original.
Then I became a mathematician in college. In the maths, it's pretty well accepted that every problem and every proof, except for the most trivial, will take at least two drafts. One for discovery that is exploratory and meandering, and one that drives from the hypothesis to the conclusion like an arrow from Athena's bow. Published proofs are never in raw form, even a single page can hide a year (or several lifetimes) of refinements and incremental improvements on partial results.
Don't be too afraid to scrap your current work and start over, no matter what you're doing. The second round is much faster, and much cleaner. Such an undertaking shouldn't be done lightly, but it's often not as onerous as most people assume it will be.
 Yes, this happened several times. Don't mess with a winning formula.
In mathematics it's hugely damaging though, the conciseness of published proofs makes it much harder for other mathematicians to see how they reached that result. And in mathematics how you got there is as important as the end results.
Especially for students studying proofs, the step from being students to being researchers is greatly impeded by not being able to see how researchers reached the end results they did.
The space in mathematics journals is limited. They really can't afford to publish anything that isn't of the form "Theorem-Proof."
What is useful is contacting people in the community surrounding a particular result, including the person (or people) that proved it. Most are more than willing to share every aspect of the problem and how their solution evolved over the course of time.
I think he used laptops as metaphor for web (social networks, blogs, etc). There are so many ideas but none of them is yours. The more your mind is surrounded with other people ideas, the harder it is to come up with something original and fresh.
Actually, I experience something of the opposite. Other people's work falls into place in my own work. Forcing me to learn new things from them and that in itself is as important as being creative. Also, the stimulation of being with highly creative people in itself is something of a rush. It just makes me happy to see other people create and succeed.
That said I believe there is a fine line between aping someone and getting inspired by someone, and that is something you have to navigate on your own. I don't know why, but I always think about Steve Jobs ( http://www.youtube.com/watch?v=CW0DUg63lqU) whenever I face something like this. It's like a metric. What can I learn from this which applied to my work makes it great?
To me 'not from our laptops' signifies that we should not jump to developing a solution immediately. For e.g. first you should think about the problem and work out a solution in your mind (you could use a pen and paper or a black/white board for help). Once you think you have a feasible answer you could open your laptop and either write down your document or in case you where thinking about a software solution bring up your IDE.
Main goal should be to think up a solution and then try them out on your laptop.
Cleese talks about how multitasking is destructive to the
creative process (at time code 6m:30s):
"But if you're racing around all day, ticking things off
on lists, looking at your watch, making phone calls,
and generally just keeping all the balls in the air,
you are not going to have any creative ideas."
I find it hilariously ironic that immediately after he
says this, the camera cuts over to two guys in the audience
clicking away on their laptops while ostensibly listening
to Cleese's talk.
Finding solutions to problems in the middle of the night while sleeping has happened to me. Usually that's how I fall sleep at night, thinking hard about a problem, or trying to build up an idea. Having things on ones mind before sleeping probably does influence what we dream and think about while sleeping.
I actually find it quite disturbing. When your conscious mind has been very focused on something the whole day it will naturally keep the momentum. That in turn makes it difficult to fall asleep and when you do the sleep is often quite thin. What I figured is that if you find a way to turn your mind off either with meditation or some distraction (for example movie or book), the sleep is much better and the next morning is usually much more productive and often the mind comes up with some suprising new ideas.
I had the trouble of going to bed but my mind was racing with ideas, and I could not fall asleep. I noticed that taking a notepad next to bed and writing down the ideas or seeds of ideas I could get them out of my mind and my mind could be at rest and I would fall asleep.
I think it releases the mind from trying to remember the ideas in the morning. When I write the ideas down I can review in the morning with the benefit of having a good nights sleep.
Just hope they don't try to replace you, and claim your life too.
The pen-light idea mentioned elsewhere is a nice addition to the notepad idea.
Most of my solutions so far usually regard trivialities. When a train of thought was genuinely worth finding in the morning, I would usually leave a relevant web search open on my phone (along with all the other things to not forget, or check later. Quite devastating is the browser choked...). Also, the display would be jarringly bright... Although, if it was a compelling enough idea, it would be enough to win me away from sleep.
"The teachers do not realize that they themselves are not very creative, and therefore they may not value creativity even if they can recognize it."
"If the people in charge are very egotistical then they want to take credit for everything that happens, and they want to feel that they are in control of everything that happens. And that means consciously or unconsciously they will discoourgage creativity in other people."