WordPress is amazing, as it is an open source platform. With that strength however, lies a problem in the fact that you have many plugins and themes, all trying to achieve different goals and all written by different people to wildly different standards.
So when problems strike, the first thing that needs to be done is some basic troubleshooting. This is useful not only for issues with Event Espresso, but any other plugins and themes out there.
These steps are in no particular order but you should try and work through them all in order to pinpoint the problem.
Theme
By disabling your theme and reverting back the default WordPress theme (Twentyeleven or Twentytwelve at the time of writing) you can see if your problem has been caused by a conflict or issue within your theme, as the default themes are coded to a high standard by the makers of WordPress itself.
If you cannot change themes due to the site being live or another reason, you can use a plugin such as Theme Test Drive to test the theme without your visitors being aware.
Plugins
De-activate all the plugins you have with the exception of the plugin that isn’t working correctly (in this case Event Espresso) and see if the issue is resolved. If not try the theme option as well.
If the issue is resolved, start activating your plugins, one by one, testing for the problem each time. With luck you will find the plugin that is causing the issue/conflict and be able to examine it in more detail or simply keep the plugin deactivated.
Javascript
Most conflicts with Event Espresso are down to Javascript: it is either being loaded incorrectly, an old version is being forced to load or something has stopped the Javascript from running. If you use Chrome or Firefox you can use the developer tools Console to pinpoint any blatant Javascript errors.
Also read here, for more Javascript troubleshooting.