I found this out today so I thought I would pass it on to help someone else with the same problem.
I have a RadGrid containing two GridDateTimeColumns (plus a few other columns) and I needed to display several rows of this grid so that all the rows were open to edit at the same time. Because of the way we managed the data, the properties for the RadDatePicker, in the GridDateTimeColumns, were set in the ItemDataBound event for the RadGrid. My problem was that once the RadGrid needed to display more than one row conatining these two GridDateTimeColumns then the 2nd and subsequent RadDatePickers would not be rendered correctly. Instead of showing the RadDatePicker popup box image it would show the tooltip text for the RadDatePicker - Open the calendar popup.
The solution was to use the SharedCalendar functionality. I created a hidden RadCalendar and during the ItemDataBound event I set the SharedCalendar property for the RadDatePicker controls and everything renders as I would have expected. have a look at the following demos for more information.
Shared Calendars - http://demos.telerik.com/aspnet-ajax/calendar/examples/design/sunny/defaultcs.aspx
Data Binding in calendars - http://demos.telerik.com/aspnet-ajax/calendar/examples/datepicker/databinding/defaultcs.aspx