MS SQL server 2016 backwards compatibility
Yes there are reported compatibility issues (difference) between level 100 and 130. Instead of me copy and paste Microsoft document I suggest you consult this document. 

ALTER DATABASE (Transact-SQL) Compatibility Level

I also suggest you list all the changes and test in your development (non prod environment) with simulating production load (covering all aspect of the application).

You might also look at Microsoft® Data Migration Assistant v3.1.


  Data Migration Assistant (DMA) enables you to upgrade to a modern data
  platform by detecting compatibility issues that can impact database
  functionality on your new version of SQL Server. It recommends
  performance and reliability improvements for your target environment.
  It allows you to not only move your schema and data, but also
  uncontained objects from your source server to your target server.


Nice article by Aaron Bertrand: 

Bad habits : Clinging to old compatibility levels