I got a new mac mini. OS 10.10.4, 2.6 GHz Intel Core i5, 8GB 1600 MGz DDRc.
I moved my licensed copy of Id CS3 from my old computer, a MacBook, circa 2007.
It works fine except for one thing. It won't spell check.
Anyone know what might be going on and what I can do to fix it?
You have two possible problems. First, CS3 is not tested and supported on Yosemite, so you're on your own and lucky to get it to install at all. Second, you say "moved." if that means anything but installed fresh from the disk or download youare again likely to have problems. InDesign does not migrate well.
I think if all that is not working is spell check you might want to consider yourself pretty lucky.