The purpose of the invisible input element is to hold the actual datepicker value (not the parsed one that you are seeing in the textbox). The input must not have a display:none style, because popup extender validators will not work with the datepicker control.
Indeed, it seems that in Internet Explorer this input pushes the control 1px downwards.
Please try adding the following CSS rule and let us know whether it helps:
margin-bottom: -1px !important;
RadDatePicker1 is the ClientID of the input element we are talking about.
the Telerik team