I have a book called Back to Basics that discusses fish farming. It mentions using a pool, but does note to make sure the water is clean and aerated. One thing it mentions is to try raising trout in the winter (cool months, since they like temps in mid-50's) and catfish in the summer (they like temps between 80 and 90).
It's something I would love to try, if I actually had much of a backyard.