I’ve used my TR for some of the software that’s on your list. Specifically, I’ve used:
Flash
Photoshop
Illustrator
Dreamweaver
Premiere Pro
In all cases, the TR handles each very well. Of course, you’ll have to realize that there are some tradeoffs you’ll have to make. For the graphics programs, you’ll probably want/need a real input device. I love the touchpad but it’s lousy for doing graphics. I use a Wacom Tablet (4x5) with my TR and it works very well. A good mouse will suffice as well.
The screen is obviously going to be a bit small when working in Photoshop or Illustrator. If you have a good grasp of those programs then you can open/close the palette using the keyboard shortcuts when you need them to optimize the work area. The same applies to Premiere Pro.
For Dreamweaver, it’s also not an issue since you can customize the layout of the program to more efficiently use the space. I don’t use this as much as I prefer Homesite for direct editing.
In terms of DV capture and editing, the TR handles this pretty well. The biggest issue might be hard drive space. I don’t say speed because the TR is capable of capturing DV without dropping frames. You’ll still probably want to get an external Firewire or USB2 hard disk to do your DV editing on as you’ll have more space and you can get faster drives. With a DVD-R/RW model TR, you can also burn DVDs straight from the system without the need of carrying extra peripherals.
For the most part, none of these programs really stress the TR except for Premiere Pro. Of course, video editing is intensive on any system. Photoshop can sometimes be slow if you’re working on hundreds of MB digital images with complex filters. Again, that’s stressful on any system. If you are going to be doing these tasks I definitely suggest getting a TR with 1GB of RAM to ensure better performance.