I'm not so certain that the issue is the definition of the term normal, so much as it is the value (positive or negative) or association (healthy vs. unhealthy) the term implies in a medical or social context.
One of the most common reasons for blurry vision while wearing contacts is that your eyes are dry. Some people have a medical condition that causes dry eyes, called dry eye syndrome, but others' eyes are irritated by the contacts themselves.
But blurry vision also can be a symptom of more serious problems, including a potentially sight-threatening eye disease or neurological disorder. Blurred vision can affect both eyes, but some people experience blurry vision in one eye only. Cloudy vision, where objects are obscured and appear milky, is often mistaken for blurry vision. Cloudy vision usually is a symptom of specific conditions such as cataracts, but blurry and cloudy vision can both be symptoms of a serious eye problem.