Hello ,
This is known issue for the 10.2 and the webdropdown. For now there are no other known issues concerning wrong rendering but this one.
In order to fix it, you should close your project, go to your folder location and delete the ig_res folder. After this open your project in Visual Studio, and open one of the aspx pages that contains an Infragistics control from the Aikido toolset, in design view. This will cause the ig_res folder to be added again to your project, and this time it will contain all the necessary styles and images for 10.2, including the arrow of the WebDropDown.
Let me know if you have further questions with this issue.
Regards,
Lyuba Petrova
I had this problem, and it persisted after upgrade to 2012.1
Having found this thread, I tried it. I'll add that you have to close and re-open the project again after the ig_res folder is automatically re-added to the project.
This also fixed a problem where a dropdown containing a webdatagrid would close as soon as the mouse moves away from the drop button. I guess the attempt to show a non-existant image was confusing the dropdown and making it close prematurely.