What are changes made to a database schema that is already in 4NF that would break applications?
Most changes are "breaking" if you aren't careful.  Any change to code for example (you mentioned triggers).  Any new or modified constraints, calculated columns etc.  

You could even add a new index and effectively "break" your application because a query that used to run sub second now runs in seconds, minutes, even hours because the query plan has changed.

Assuming your code is written to always specifically name columns will probably make adding new columns reasonably safe and adding a table almost always is but you still probably want to test how each change to your database affects your application and it's performance.