Well my card says 1080p is supported, and even on videos that aren't low quality things aren't as clear as they are on my other monitor (which is set up right next to it in 1024 x 768 resolution)
It sounds to me like the video is just not high enough quality.
For example, if you watch 1024x768 video on a 1024x768 monitor, it will look perfectly sharp because it is using every pixel on the screen.
If you watch that same 1024x768 video on a 1920x1080 screen, the video will look kind of blurry. That is because it is taking the 1024x768 video and stretching it to fill in 1920x1080 pixels. Does that make sense?
Try finding a video that is 1080p quality, and then watch it on your TV. That should look very sharp. If it does not, then something else is the problem. But to me this just sounds like low-res video being played on a high def screen, and of course it looks kind of blurry.