Mac mini and Sharp Aquos

Your primary concern is choosing the type of connection to use for your TV. If you are using a separate audio tuner or surround sound, you can use the included adapter that provides a full sized DVI port. You can then use a DVI to HDMI cable to get the video to your TV. If you wish to send both video and audio to your TV, particularly via HDMI, you can use an adapter like the one sold by Kanex:
http://kanexlive.com/products/item-id-3495.html
Once you've made that connection, you will probably have to use a scan setting on the TV to allow the desktop to properly fill the screen. If you can provide the exact model number of your TV, I might be able to find the manual online and give you an idea which setting may be most effective.

How old is that TV? My older 32" Aquos did experience issues with the scanning being off.

Does the band run completely left to right across the bottom of the screen? Is the band video, or snow, or a solid color or ??? Is the band all the way at the bottom of the screen, right up against the bezel? If so, about how far up into the picture area does the band go?

You mentioned the band is present with or without overscan being checked. Is the size of the band affected at all by this setting or is it completely unaffected by the overscan setting?

Just needing more info to help understand what it might be.

I use the Kanex Mini-displayport to HDMI w/ 5.1 audio. My TV is a Mitsubishi LT-52246. This worked right out of the box. With the Mac mini on 1080P it worked fine but the text was too small. I have played with different resolutions on the Mac to find a resolution which works and is readable. I tired the 720P resolution on the Mac but then the top of the screen was cut off.
In the display adapter software interface under options I only have overscan available there is a TV option which is greyed out.

Any thought?