Having defined (because it appears none are setup for Change domain in OOTB DB) the default filter queries for collections such that they display on tabs at the bottom of the WebDesk main window (where required) I've noticed that the column order does not match the order that the columns are in the original filters in console (which do show correctly).
My suspicion is that they are showing in in Webdesk in the order the attributes were selected/dropped onto the filter design when the query was created in Query & Report Designer and not in fact the order they are actually in in the query post edit and save; ie columns subsequently reordered in the designer.
Can anyone confirm this and if so is there any easier way to affect the column order in WebDesk short of dropping every attribute off and back on again?
Well problem 4483 seems to describe your symptoms and is listed as fixed in 7.4 Maybe it's a slightly different problem though. I'd be interested in knowing what your local support team come up with as this fix was very much welcomed.