One of the most exciting features of the Template Designer is the Live Preview. As you change any blog template setting using the Designer wizard, in the upper pane, you immediately see the effect of the change in the lower pane. That is the intended effect, when the wizard works.
The Template Designer, as most Blogger blog maintenance wizards, runs in "Blogger.com". The live preview window, however, runs in the domain where the blog is published. This requires that both "blogger.com" and the blog domain have trusted status, and causes a vulnerability called cross-site scripting.
Blogs that are published to BlogSpot require XSS permitted to "blogspot.com", and blogs that are published to custom domains require XSS permitted to the domain URL. Anybody with any serious concern for security permits neither, by default.
If your browser is Firefox, and you use NoScript for add-on security, you'll do an "Unsafe Reload", if you want your Live Preview to work. You do the "Unsafe Reload" from the NoScript XSS submenu, either from the status bar NoScript icon, or from the XSS alert bar which NoScript adds at the top of the browser window.
When you select "Unsafe Reload", you'll get a popup warning, with the option "Don't display this warning again". If you select that option, the "Unsafe Reload" should be expected to run, next time, without showing a warning. In some cases, though, after you select "Don't display this warning again", the "Unsafe Reload" icon will not be displayed again. This will leave you unable to run "Unsafe Reload", the next time that you start the Template Designer.
Internet Explorer uses a Zone security. You will have to designate the domain where your blog is hosted as being in the Trusted Zone, then ensure that XSS is permitted for Trusted Zone domains.
Cross Site Scripts are a problem that's sort of unique to the Template Designer wizard. There are many other security problems, though, that the Template Designer wizard shares with several other Blogger features - like Blogger login, Commenting, and Stats. Layered security must be properly setup on your computer and network, if you wish to use Blogger effectively.