Migrating SQL server 2008 to 2016
Before you migrate any databases, run 'Assesment' in Data Migration Assistant. It'll point compatibility issues between versions and also show you some best-practice suggestions. Then proceed with actual migration. 
I noticed that one thing that DMA doesn't do, is to raise a warning if a database is running in Sql Server 2005 (or earlier) compatibility mode. Sql 2016 does only support compatibility modes 2008 or higher. So don't trust it blindly as there may be more aspects it ignores.