TL;DR
In this post I will explain what should be checked after Ruby on Rails minor version upgrade. Minor version upgrades are usually connected with security releases.
As I am subscribed to Ruby on Rails security Google group, when I receive information about latest security issue, I need to act very fast. Update must be pushed to production almost immediately, so there is no time for extensive regression testing.
How can we do quick test and be sure that everything still works as before upgrade?
Heuristic 1. Rails upgrade was extensively regression tested.
That heuristic proved itself to be always true.
Heuristic 2. Inspect Gemfile.lock to be sure that only Rails gem is upgraded.
How do we actually upgrade Ruby on Rails?
Edit gemfile:gem 'rails', '4.2.5.2'
bundle update rails
Investigate Gemfile.lock changes using git diff to see what else was updated beside Rails. If some other gem (not part of Rails) was also updated, check, using Google search, possible issues for that gem that are connected with Rails upgrade.
Heuristic 3. Search Google for Ruby on rails upgrade to n.n.n.n version issues (bugs, problems)
Conclusion.
For minor Ruby on Rails upgrades, using those three heuristics, you can do regression test in smart and quick way.