I purchased Studio HD Ultimate, and tried to install. A message shows up: Data error (cyclic redundancy check), then the window closes. How can I fix this?

This means yo have a bad disk, or file. Are you installing from a CD or from a download?

I have the same problm with Pinnacle 16. I am using a disc, it worked fine last year but now it won't install. I can install the content and all, but Studio gets me "cyclic redundancy check". If I do have a bad disc, how do I get another? If I do have a bad file, how do I find which one?

Welcome to the forum. 

Try copying the contents of the disc to your hard drive and installing from there. 

Why are you re-installing?  Were you having problems with the installed program?  Are you installing on a new hard drive?  When are you getting the error message?  What do you mean when you say that you can install "the content and all".