I have almost the same.
After updating to version 2.4, many pages will not load completely.
The logs are constantly recording error «PHP Fatal error: Out of memory (allocated 65011712) (tried to allocate 56145 bytes)»
Rolled back to version 2.3.5 – it worked fine.
@limych That’s a common WordPress issue. You can find a solution here:
http://codex.wordpress.org/Common_WordPress_Errors#Allowed_memory_size_exhausted
@aguatacuperche Could you try the solution I mentioned above? If that doesn’t help, I would suggest that you try to log in to your site via FTP, delete the existing Jetpack plugin folder, and reinstall manually:
http://codex.wordpress.org/Managing_Plugins#Manual_Plugin_Installation
If you still experience issues, we would need to check your server error logs to learn more about this “white screen of death”. If you don’t know how to access your error logs, your hosting provider should be able to help.
Thanks!