Thanks for the suggestion. I have tried deleting the cache manually, but I have not been on the specific page when I did it. I will try that again. I *have* tried going through the Admin menus to manually clear the cache and garbage collection, and that had inconsistent results.
I'm running WordPress 3.3.1 on a shared hosting system. It's a pretty vanilla install running a child theme of Twenty-Eleven and a handful of plugins. I'm the only user so far, but I will be adding several more editors in the next couple of months.
Waiting for garbage collection doesn't seem to work. After changing the page content from one Gravity Form to another, the cache was still serving the wrong page after 2 days.