Verify all Stored Procedures
No, there is no built-in way to do this within SQL Server. As Marian stated, you could recompile all of your procedures to be sure they're still valid, but this doesn't prove they'll still work (and don't forget that deferred name resolution makes this validation less than stellar anyway). However you can use other tools such as SQL Server Data Tools (SSDT) to help facilitate unit testing.

Just like changes to your application, if you change your schema, you need to test those changes. How automated you make your unit testing depends on the complexity of your schema, the consuming application(s), and the number of permutations possible for stored procedure outcomes (including both explicit input of different parameters or different parameter values, and implicit input such as time of day, state of the system, specific data at rest, etc.). You have to keep in mind that in some cases you will expect the stored procedure output to stay the same, but in others you will actually expect it to be different.

Some potentially helpful links (a couple culled from a question on SO geared to testing a single stored procedure):


TSQLUnit for unit tests
T.S.T. the T-SQL Test Tool