I also have a one-year-old Samsung and I managed to get it to not overscan for at least one input. Put your Mac Minis HDMI into the HDMI 1 / DVI input and then select the input in the Source menu on the TV, press Tools on the remote, and chose PC as the name of the input. This magically turns off overscan. Hope it works!
Did that already; no joy. It's not a problem because of the overscan slider in OSX, but it was a huge annoyance before I upgraded the mini (you need the built-in HDMI to get the overscan adjustment).
Unfortunately you're most likely losing resolution in this case. If, for example, your TV is cutting off 3% of the image, then the video card is scaling your whole desktop down from 1920x1080 to ~1862x1048, which will result in more than 3% apparent resolution lost due to less-than-optimal interpolation.
