...the mini was set to output a resolution which was too great for my TV to display.
I seriously doubt this will be a problem with one of the newer Minis or most HDTVs--the HDMI port should tell the mini what resolutions are supported, and nearly any TV with an HDMI port should do at least 720p, which is plenty for the MacOS.
That said, while this would work perfectly fine (I've used my home theater mini on a 37" TV as a backup desktop on occasion), if you're doing stuff with CS5, this sounds like a bad idea to me.
Gaming and movie watching, obviously just fine--they're both the sort of thing for which the bigger the screen, the better (in general), and you don't mind sitting far away from what you're doing.
However, if you're using CS5, normally you're doing something that requires a reasonable degree of pixel-level precision (and, in most cases, color fidelity as well). Given the incredibly low pixel density of any HDTV (other than unusually small 1080p sets, in the <30" range), if you sit at anywhere near the usual monitor distance you're going to be looking at an immense blurry image, and if you sit even a little too far away, you're going to be squinting at invisible pixels.
Essentially, at the normal roughly arm's length you sit from a monitor, the pixels of a standard monitor (in the 100-125ppi density range) are visible, but not clearly; lean forward a bit, and you can see them more clearly, for precise work; lean back a ways, and they disappear entirely.
With a TV--let's say a 40" 1080p display--you're going to have to sit somewhere around 5 feet from it to get pixels in the same visible size range as a monitor, and leaning forward or backward won't really make any difference, since it's proportionally much farther away--you'll have to get up and walk closer to see the pixels, if you need to do something precise in Photoshop or whatever.
Then there's the fact that most TVs (with a few high-end exceptions) use panels designed for high contrast, deep blacks, rich colors, and motion. Which are crappy, crappy things if you're trying to do color-accurate work in Photoshop or Illustrator, even with calibration.
There's a reason Apple uses IPS panels in all their displays (other than the laptops)--they cost at least three times as much as a comparable TN panel, and wouldn't look as good displaying a movie or game (slower response time, less contrast), but they're drastically better when it comes to color accuracy.
Bottom line here, sure, it'll work, and it'll look great playing Portal or watching a movie. But unless you like sitting very far from the screen and don't care much about color or precision in CS5, it's probably a bad idea for graphic-specific computing.
