I worked with tech support on the phone (2.5 hours) and we did not solve the problem, however, I encountered severe Keynote problems in the past and it was font related.
One of the first things I did when the problem started was to go to FontBook, select all the fonts and run a Validation. Then, the fonts with marked with an X, I removed. Unfortunately the problem continued and it seemed to be getting worse. Now, I couldn't save files without a warning coming up and I was losing the photos that were placed in the doc.
The tech had me do a safe boot, open a new user, etc. The new user worked but who wants to switch back an forth between users just to do a Keynote preso??
As is often the case when you are at your wits end, you go back over things you have already done. I went back to FontBook and ran the validation again. Much to my surprise all the X fonts were still there. Hmmm. So, I went in and manually deleted these varmints.
Problem solved. Now the corrupt files are still corrupt but I was able to create a new presentation, clean from errors.