Using the UpdateListItems webservice from jQuery creating an item in a custom list returned the error: "0x80070005 The operation failed because an unexpected error occurred. (Result Code: 0x80070005)".
The webservice call worked correctly for site collection admin and site admins but not for ordinary users. The list was configurd with "Add item" and "View pages" permissons for ordinary users which should provide correct access for the UpdateListItem method.
The problem with the list was that is was configured with a "None" value for the property "Edit access" (General settings --> Advanced settings). After changing it to "Only their own" the method call succeeded. So the "Edit items" property was messing up a "New item" method call.