You can download the Microsoft specification of the XMLA protocol here: http://msdn.microsoft.com/en-us/library/ee320606.aspx (more than seven hundred pages).
In general, there are two types of errors:
- Global ones, that either prevent the request from being executed, or prevent the server from returning anything useful (e. g. syntax errors),
- and local ones, e. g. within a single cell of a response to an MDX SELECT request where the general result structure is returned. In this case error objects may be returned e. g. in one or several cells instead of the result. An example would be an error an prevents the server from calculating this specific cell value, like a reference to an unknown element in the definition of a calculated member.