@tandava:
Despite tzapits's reply above, they don't have the Custom Design upgrade.
@ tzapits.
The option raincoaster suggested doesn't do anything by itself: it auto-corrects unpaired HTML tags in posts if you edit the posts after you enable the option; and it cannot correct text widgets. But I checked the sourcecode of your page, and you don't have such issues.
The world clock you've got in one of your sticky posts is wider than than the main column of the theme. You should remove that post and put the clock in a no-sidebar static page.
In your sidebar you're displaying lots of images hosted elsewhere, and some of the originals are a lot wider than the width of the sidebar column; example:
http://www.kodipheet.gr/images/spectrum2.jpg
Explorer doesn't understand the 'regular' code for downsized display. A temporary fix might be to change the coding of all such images from this:
<img alt="DESCRIPTION HERE" src="IMAGE URL HERE" class="alignnone" width="100" height="30" />
to this:
<img alt="DESCRIPTION HERE" src="IMAGE URL HERE" class="alignnone" style="width:100px;" />
But the real fix is different. You're displaying an impossibly large number of items on your sidebars, so your blog pages take too long to load (and that's a page ranking factor as well). The more the items linked to from other sources, the worse. So, two suggestions:
1. Ideally you should copy all the sidebar images to your computer, scale them down in an image editing application to the right pixel width, upload these copies via Media > Add New, copy the file URLs that will show up, use those URLs in the widgets.
For maximum pixel width see here:
http://wpbtips.wordpress.com/2010/08/10/coraline-layouts-and-mullenweg-pearson-dispute/
2. Cut down on widgets: transfer some of the stuff to static pages.