I teach front-end web development at Harvard University Extension School, and I teach via video at O’Reilly Media. This is a topic frequently on my mind.
Unfortunately, many colleges and universities are still teaching Dreamweaver as an industry standard, never touch on responsive design (or mobile compatibility in any form), and they may be still teaching XHTML or be hung up on making websites compatible for IE6.
Every employer has different workflows, different core browsers to target, different philosophies concerning mobile device support, and different coding and version control standards. Know the basics, get some critical thinking skills, learn how to learn technology, and you can learn anything after graduation on your own.