Is there any way to blur all page (for example set new background and give it to the foreground with z-index) and focus certain div (let’s say error message) with jquery/javascript? Do you know any plugin for that purpose?
That’s what I wanna get:

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You can use the jQuery UI dialog and use CSS to change the overlay div background with a blur background image, like here:
http://css-tricks.com/examples/BlurryBackgroundEffect/
–or–
You can use the jQuery UI dialog mixed with the CSS Text blur effect found here:
http://motyar.blogspot.com/2010/04/blur-effect-with-css-and-jquery.html
However, I assume this will NOT be backwards compatible with non-html5 browsers.
Here’s a JS fiddle for proof of concept: http://jsfiddle.net/khalifah/vgGtK/
Here’s one with the style I think you want: http://jsfiddle.net/khalifah/7L5jG/