Sorry Michelle, this could be a little more complex than you’d like. I’m assuming you don’t use the same markerly script as I did (it’s something I added at the footer of my site which allows visitors to micro-share individual media content or text snippets through social channels) – you’d know if you added such functionality yourself.
In your case I suspect the problem lies with one of the 3rd party plugins used on your site.
The best way to check is to ‘disable’ every plugin, leaving just Jetpack installed, then check the Carousel function again. If that doesn’t work, then switch to the ‘Twenty Thirteen’ theme that came with WP3.6, while keeping just Jetpack enabled, then try the carousel again.
If after disabling all the plugins it cures the problem, then you know the problem lies within one of your third-party plugins – in which case enable each one-by-one until you find the offending plugin (then disable it permanently, let the plugin author know about the problem and wait until it’s fixed – or try an alternative).
If disabling plugins doesn’t cure it, but switching to Twenty Thirteen does, then you’ll need to examine the theme – again if it’s one you’ve purchased off the shelf then contact the theme author and let them know, in most cases they’ll already be working on a fix.
One of the reasons for such a problem is where the theme loads its own version of jQuery (the main javascript library which enables the fancy parts of your site), this will conflict with the version loaded by WP3.6 and may cause functions like Jetpack Carousel to stop working. The solution is to either wait for a fix from the theme author, or change your theme to one which follows the correct practice.
p.s. if you’d like to switch your theme, but only for you (as admin) rather than changing the site your visitors see, then download a plugin called ‘Theme Test Drive’ – this allows you to run two themes at once – one for you and one for your users.
Hope that helps.. ??