Changing the SQL Server Compatibility setting for individual tables/columns, which have retained older settings
Compatibility levels are set at the database, not at the table or column.

You might be thinking of collations, which are set at the column level.  You can't simply change the collation on those objects - you have to build new objects with the right collations and push the data into them.

You might also be thinking of deprecated datatypes like text, ntext, image, or vardecimal.  You don't have to change those yet, but you'll have to fix them before a future SQL Server version.