CPU for Video editing

Ok - I'll try to answer a bunch of these

1) Laptop for video editing?
I'd have to reccomend an apple, but in general something high-powered will be ok. Make sure it has something more than integrated graphics, and plenty of hard drive space/ram.

2) Pentium 4 proc vs. Pentium M (mobile)
They both offer different things, although the mobile processor is more desirable in laptops because of its power consuption. The p4 is essentially a desktop processor in a laptop. With this comes all the heat, power usage and power of a desktop. The M proc. runs on much less power, so your battery will last. It generates less heat, and laptops carrying such a processor are much lighter than the p4 variants.

3) Dual core vs. Single core
YES! While you won't be able to play doom3 and author a dvd at the same time, it's much better at multitasking. For video editing I can imagine you would need to run long operations and still want to use your machine. In laptops... you're probably not going to see dual core make an appearance apart from the macbook pro.

My two cents?
Apple. I would wait and see how the macbook pro pans out, but if all goes well you will have a highly mobile machine, great screen, 4 hour battery and dual core power. (not to mention the dvd burner) If you have to get something now, the g4 powerbook is still quite solid, and packs plenty of power into the shell. Granted this is for laptops - if you wanted a desktop it gets much more complicated. Right now I'm thinking look at the macbook pro, because the x86 laptops havn't seen the new dual core procs in yet.

Hope that clears a bit up, and is accurate
Feel free to ask any more questions
-Bill