Hi guys, we run a web app called Tailor-M (www.tailor-m.com). It's a B2C application to help consumers find a tailor. We often run into issues with bugs related to specific devices. For example, after we deploy some new features, everything seems to be working on my iphone 6,
I'm surprised you are having such significant issues. As a 'broad' generalisation, modern UI frameworks are designed to be quite adaptable across browsers and devices, and standards compliant, particularly for simple form update type applications.
Having many issues in this space implies to me that either the app is very complex, or uses some unconventional methods or technology, in the way it's been built, or a custom framework etc.
As a rule, I would always do some level of testing across devices for UI changes. For my software I always test across Chrome, IE, Safari, and iPhone / Android, using BrowserStack and physical devices. Occasionally we will get a minor layout quirk, like text aligning in the wrong place, which requires a specific rule for a particular browser / display type, but never the extreme of the application not-working at all.
The most aggressive issue I have seen, is have site content shown inside iframes. This did not work well across devices. iframes seem to not be very well supported (originally introduced by Microsoft as opposed to being a general standard, and so implementation has been inconsistent).
Thanks for the sharing.