Beyond the Hammer Test results mentioned by Adrian, which is basically running your Apex test cases before and after the release, you will need to have a separate process for evaluating each change or new feature made in a seasonal release.
For example: Create Shortcuts to Your Top Salesforce Pages with Favorites
This is specific to Lightning Experience and the general navigation. Between that and being a new feature your Apex test cases are unlikely to even consider it (if at all for UI features).
So, in summary, your Apex test cases will give you some indication is anything has affected you code. There could still be side effects that you just can't test for.
The only way to know with reasonable certainty is to run through all the required parts of your app manually. You might be able to automate some of the UI intereactions to test everything. You would need to make the call if the effort to do that is worth the benefit.