Can a random mild virus give you blurry vision?

A random mild virus : You could get fever and dehydration as a result, which could certainly make you dizzy with somewhat blurred vision. You could also get viral conjunctivitis or even meningitis or encephalitis. I don't mean to scare you, but it's best that you see a doctor.

Yes: Several viruses can affect the optic nerve, such as shingles, Varicella Zoster. Other viruses and causes infection of the conjunctiva, sclera, iris, Facial nerve, Abducens nerve, which can lead to bulbar neuritis, conjunctivitis, keratits, Bell's Palsy, and iritis, which can all affect vision.