Adobe Flash has poor playback performance on machines with weak CPUs and no hardware to decode videos (= most netbooks).
The GMA500 graphics in the Mini 1010 and Mini 12 should be capable of accelerating video decoding, but the Mini 1010 and Mini 12 also have HUGE drawbacks. The 1010 has poor IO performance, and the Mini 12 has what is essentially an iPod hard drive (=crazy slow).
Netbooks with the more common GMA950 or GMA3150 graphics (Mini 9, 10v, 1012, etc) only have video decode acceleration via the optional Broadcom Crystal HD decoder card. I think this was an option on the 10v, but if you didn't opt for it from the factory, you might be missing the slot. The card should work in the WiFi slot instead, but then you'd need a USB WiFi adapter.
A final option is better software. I can usually play 480p (DVD-ish) web videos perfectly on any netbook. I just have to download them and play them in a separate player. This is easy for many, but not all, sites (I played a test vid from nba.com easily).
In Linux at least, the Adobe Flash plugin caches many web videos to a file, so I just queue up the web video, pause it, then open that file in an external player. There are also web browser extensions to aid downloading.