Custom theme not compatible with 3.2.1 – how to fix?

I took on a client after someone built the site. The theme is a custom theme and this is the first time the theme wasn’t compatible with a WP upgrade (3.2.1). I’d like to fix b/c I know the latest version has to do with speed and this site needs it. But, I”m not sure what WP changed to know what I need to fix.

Any guidance about how to go about fixing theme to work with new, 3.2.1 WP version so appreciated.

Thanks much!