I ran into what seems to be quite a common problem where the JCE buttons won't load in the front-end. The JEvents FAQ page only seems to apply to Joomla 1.0: it wasn't very helpful for my 1.5 site anyway

After a bit of thought I realise that you need to set up a group in the JCE administration for whichever user level you've set up to create events (in my case this is Registered users). The great thing about JCE groups is that you can change the toolbars by group so you can restrict what the front-end users have access to.
Now that I've set that up everything is working nicely, except that if I set the front-end editor to open in a popup, it will cause a couple of small problems if you create a menu link to the add-event form. Firstly the site template doesn't load, and secondly the "cancel" button leads to a blank page. Not a big deal for me - I just turned off the popup.
Cheers,
- Dave