On many sites, mobile users represent 90% of the site visits.
Embedded content often struggles there, since they may not be as responsive as your site, or respond in the same way.
Test, test, test. And test again.
It matters far more than you think. If your embedded content isn't working on mobile, it's not working. And if your site's not working on mobile, it's not working at all. Period.
Common problems;
Also, I recommend that you test a recent iPhone, and a recent Android phone, both. Go for devices that are 2-3 years old, so that you're getting a mainstream view, with a mainstream screen-size.
You'll notice the tiny differences in screen resolution, and the differences in browser ( Safari v. Chrome ) can have a huge impact on whether your site is usable on that device or not.