I wish to develop simple slideshow in wordpress with jQuery. It really works nice in most browsers except IE.

var blockShow = function(element,nav,duration) {
  //alert(element);
  container = jQuery(element); // but in this fuction throw error: Object doesn't support this property or method
}

// this works
jQuery(document).ready(
  function() {
    if(jQuery('#header-slideshow')) {
      blockShow('#header-slideshow');
    }
  }
);

UPDATE: I didn't remember to express: outdoors Wordpress it working perfectly. In IE and otherwise, therefore it need to be something in Wordpress.

from the experience if something isn't employed in ie, but is otherwise, its among 2 things.

1 - you've some syntax slightly wrong somewhere - mayde invalid html (try validating your html and css http://validator.w3.org/) an additional comma or something like that. Other browsers are usually better at disregarding minor syntax bugs

2 - you've some type of conflict with wordpress' existing scripts. Try reorganising the burden orders.

without seeing the particular site, the only real other factor I'm able to recommend would be to support your template, and methodically remove wordpress elements 1 by 1 until it really works! It will help identify the issue code.