If you're doing an upgrade of the Master Data Services database to SQL 2016, there were some radical schema changes inside, and the upgrade may fail with an error:

Microsoft.MasterDataServices.Configuration.ConfigurationException: The CREATE UNIQUE INDEX statement terminated because a duplicate key was found for the object name 'mdm.tblUserMemberCount' and the index name 'ux_tblUserMemberCount_User_ID_Version_ID_Entity_ID_MemberType_ID'. The duplicate key value is (x, x, x, x).

It's worth checking the data (with the usual warnings about taking a backup) but if you don't have time or money to call Microsoft to sort it out:

Delete From
With Cte As (
		Select ID, Row_Number() Over (Partition By User_ID, Version_ID, Entity_ID, MemberType_ID Order By ID) As RowNumber
		From mdm.tblUserMemberCount
From	Cte
Where	RowNumber <> 1

I've also seen a second post-upgrade error where a single user was able to access the front end but would receive a random error when clicking into Explorer:

In this case using the MDS refresh cached information button, and using the Explorer refresh buttons, or altering compatibility view settings did not fix anything. What fixed it in the end was a full delete of the temporary internet files and cookies.