I had this error "The operation could not be completed" when trying to connect to a SharePoint List as an external data connection in InfoPath today.
Show Details just says "Unable to connect to the SharePoint site."
Figure: The message box really doesn't tell you anything.
Turned out, I was testing with a new managed path on http://server/sites/TravelFunds/ But the web application did not have a site at the root path. So the quick fix was to create a new team site (blank site might work too) at the root path http://server/ and then come back to InfoPath, and http://server/sites/TravelFunds/ will now work as expected.
This was one of many posts that I read regarding similar problems, and the one that actually applied to me. http://vspug.com/ssa/2010/03/15/infopath-2010-cannot-connect-to-sharepoint-2010/