There are two trivial cases:

• A new column is added to the dataset: If there is a new column in the dataset, you'll see a new field in the Data Source. You don't have to do anything.
• An unused Field is removed or renamed: If there is an unused field in your Data Source that is deleted or renamed from the dataset, you won't even notice it. It'll simply be suppressed on renamed in the Data Source.

The last case, when a field that you use in Tableau is deleted or renamed in the dataset, is a bit more problematic.