Actually I determined the problem was due to your Telerik Visual Style Builder. I used that tool to change colors, etc. and in the code created from your tool it was applying this style in both the date picker and the combobox with regard to the sprite:
Which makes sense because there is no 'Common/radActionsSprite.png' in my project.
.RadPicker .rcCalPopup, .RadPicker .rcTimePopup
border: 1px solid #cdcdcd;
/* background-image: url('Common/radActionsSprite.png');*/
.RadComboBox .rcbArrowCell a
background-position: -11px -58px;
Once I excluded those lines the problem went away.