The only way to ensure a good-quality application is to test it on each platform that you aim to support. This is the same for system applications (which could aim to work on Linux and Mac, for example) and for web applications (each web browser could behave slightly differently). However, the variance in graphical desktop environments can be substantial, potentially leading to many different versions of your user interface. Additionally, setting up each of these platforms probably requires more computers, or some complicated multiple-boot setups. Virtualization offers a good solution here: where possible, you could create virtual environments to mimic each of the operating system installations you need to test on.

If you are including Linux or similar open source operating systems, remember that users are free to choose different desktop environments, each of which have a different look and default behavior. For example, if you are supporting Ubuntu Linux, you probably need to test the default environment (Unity) but also the very common Gnome alternative. There are many different desktop environments for Linux to consider, including KDE and Xfce, which are also very popular, each with a different look and feel and often with different workflows to consider.

Even if you intend to focus support on just Windows and macOS, you will still need to consider what versions you will support. The look and feel, and even default interactions, can change from one major release to another, so will you aim to adapt to these nuances or instead just provide a great experience for the latest version of these systems? Be sure to record which operating systems and versions (and even desktop configurations if you are going to target Linux) you will support and set up a test environment for each of these, if possible. It will help in the long run!