Removed blockUI configuration in compat JS code since the block UI code resides solely in core.
This change uncovered another problem with the overlay used to render the busy indicator. The JS code found in the pseudo URLs of the iframe used as overlay didn't render correctly. The fix changed the JS code to pass in the markup into document.write method as it should have been in the first place.

Once the blockUI configuration parameter was removed another three errors popup while reloading the page. Screenshots 2,3, and 4 show the type of errors.
All these errors seem to indicate that compat.js and icefaces-compat.js are not loaded properly. Looking at the markup I could see that GoogleMaps JS reference would be rendered just before compat.js and icefaces-compat.js. After modifying GMap component to not render its JS reference all the mentioned errors went away. It seems that the popup rendered by GoogleMaps mentioning that the key is not valid for the site interferes with the loading of the subsequent referenced JS code.
So, really this errors would not occur if the GoogleMaps key would be configured correctly during deployment. Also the errors would show up only if IE's Reload button is pressed, hitting Enter or Go on the URL will always work without any issues.

There still an issue remaining during reload. When selecting the 'Popup Panel' panel in component-showcase and then page is reloaded an 'Operation aborted' popup is shown. This type of error is described here: http://support.microsoft.com/kb/927917 .
Looking closer at what popup related code is evaluated during page load I manged to find that Ice.iFrameFix.start() function is indeed invoked and it has document.appendChild() method invoked in its body.
The fix applied was to change slightly the code to use element.inserBefore function. This trick was already used in other places in extras.js.