A big part of my job is to maintain a page that has both a logged-out and logged-in version, combined with desktop, tablet, and mobile versions. So, at least a 2 x 3 matrix of visual variations to keep an eye on.
One tool I found to be quite useful lately is the Blisk tool . It's a wrapper for Google Chrome and how it works is that you define a set of devices and it will render the view of that page on all of the devices simultaneously.
It is basically like having multiple dev tools opened at the same time.
I usually have a set of desktop - laptop - ipad - iphone. You will need quite a big monitor to use for all the tasks. In general, I use it to give things a last check before sending my code to review.
Most likely there are multiple tools like this one available out there, but this is the main one helped me quite a lot lately.