I see a couple of situations where I use critical listening - extensively when purchasing new components and again during set up in my home listening area.
For me the most important thing is to have a set of 6 or so musical tracks that I know very well, and that represent the different parts of the audio spectrum. Bring with or have AD stream, so that you can listen for reproducible instruments/sounds from the component being auditioned. Same thing when setting up a listening area (moving things around, adding a new component).
Critical listening for me evolved into musical enjoyment once things are just right.