Brandon,
I have been looking into writing unit tests of late, though it is still a work in progress. Selenium isn't limited to Python - you can use multiple languages. There's actually a GitHub using Intern + Selenium for ArcGIS (this looks geared towards unit/function testing):
DavidSpriggs/intern-tutorial-esri-jsapi · GitHub
Intern is a JavaScript test stack... if you're already writing JavaScript map apps, this may be a good choice, too. I know most GIS people are familiar with Python, though. I've worked for an organization that employed Python/Selenium for automated QA - repurposing for load testing is another benefit of writing your test users:
How to perform load testing using Selenium WebDriver? - Stack Overflow
If you aren't familiar with web crawling/scraping/mining, the basic concept is that you would automate browser actions in your application, like clicking on buttons, submitting forms, navigating, etc. This would be done by writing a test user/script that would interface with your map and follow a predetermined test path.
You could write into the script logic to check whether a page loaded, the output was expected, etc., but with Selenium, you can spin-up multiple test users/scripts at the same time, so load can easily be tested on the server (maybe using Perfmon?).
Here's a tutorial on Selenium + Python:
http://engineering.aweber.com/getting-started-with-ui-automated-tests-using-selenium-python/
Unfortunately, you would need to code your test users - I am not familiar with any of the commercial products that don't require coding, though I know they are pricey.
