The problem with that video is that it's a marketing video showing the ideal circumstances (I'm on a Transformer right now, been using it for a year). The problem comes when ANDROID enters the mix. They don't show the sluggishness, the 5-10 second delays, the order of your commands getting mixed up, or the fact that any program at any time can bomb to the desktop because the OS is flaky as hell. The Java Virtual Machine that runs all software goes batshit insane at random intervals and makes any app run afterwards do random things until you reboot.

They also don't show when you get a firmware upgrade overnight that breaks every single app, and you have to wait for each of them to update with a specific fix for your exact device model + firmware. Asus android forks are also prone to random reboots, it took them 4 firmware patches to somewhat fix it, at the cost of other issues being introduced. 1 firmware patch even broke the keyboard, and random characters would come out for each keypress.

An Android device cannot be trusted to do the simplest things. Everyone has flaky hardware, with flaky custom forks of a flakier OS. I say this as a guy who has 3 tablets, and wants to get a Nexus 7 soon. It's just not there yet as a serious OS. You'll find that out the hardway when your note software bombs to the desktop without warning and you lose everything, or another app like G+ (That never goes away) opens in the background and the JVM bombs and corrupts all the memory in every app. There goes your notes!

A netbook running windows at least has a stable OS and stable software.

Heath, Asus makes the Nexus 7. It's a smaller transformer product without the dock or branding.

How well do most capacitive styluses work?

An obvious one to look at would be Samsung's Galaxy Note 10.1 that was recently released, that supports a pressure sensitive stylus (or if you want something smaller, there's the Galaxy Note smartphone). The Galaxy Note seems to have been designed around the idea of taking notes, so hopefully also has better software support as standard, and wasn't simply designed for consumption, as Bregma says is a problem with many tablets (well, I haven't used a Galaxy Note, but it seems worth taking a look to see what if offers). The Microsoft Surface will also do so. (The problem with most capacitive screens has been that they aren't pressure sensitive and don't work with most styluses, unlike the older resistive touchscreens - the "capacitive styluses" tend to have a rounded end rather than a pointed end. But Samsung and MS appear to have now solved the problem of making touchscreens with the best of both worlds.)

If you're looking at the larger side of tablets, and are willing to wait, I think it's worth waiting until Windows 8, as I suspect we'll see plenty of interesting new devices to choose from, which will have all the functionality of full blown PCs. (This is my plan - currently I have a Samsung netbook, but I'm looking forward to the idea of something even more lightweight, with touchscreen, but still with a real keyboard and a full computer non-phone-derived OS. And hopefully with a resolution higher than 1024x600 too!)

OTOH if you just want a device for one thing, and are okay with a capacitive styluses, the Nexus 7 looks to be a great tablet at a decent price. (I have the Galaxy Nexus, basically a smaller phone version of the same thing.) But you'd need to get your own note-taking/doodling software, as vanilla Android doesn't come with any. Do you currently have an Android smartphone? (As in, an obvious thing would be to try out software in advance, then it's just a question of if you want a larger screen - otherwise, it's a case of asking for recommendations.)

Were you running Google's factory images, or images that had been modified by the manufacturer of the device? I ask because my first Android phone was made by Huawei, and had a custom image that they had modified, and it was flaky as you described. Since then I have only used Nexus devices with images provided by Google and have not had any instability at all.

There is really no such thing as a "Google factory image." Every single Android image installed is a custom fork. Android is not Android (heh, I call dibs on the initialism for "Andoid is Not a Universal Standard). Not only that, but the OEMs generally have no clue, or even desire, to support their images in the long run. If you're working with a typical OEM and need the source for their image, you get a zipfile of the developer's personal source tree. Not even a git repo you can run diffs on. It's a <offensive adjective> nightmare.