Got my ESA after the Work Capability Assessment in July but was placed in the 'Work' group rather than the 'Support' group (even my local job centre thought that was wrong).
So I applied for a 'Mandatory Reconsideration' straight away with the help of my local Citizens Advice Bureau and just heard I've been successful.
If you're dealing with a DWP decision get the advice of the CA to prepare your case. If I'd gone ahead and used the arguments I thought were obvious I might not have won. The CA gave me a solid case to present using the DWP's own terms - you've got to fight fire with fire.