The S/N dichotomy is the most sketchy of the MBTI dichotomies because there are supposedly so few intuitives relative to sensors. In terms of information processing, the key for intuitives is the ability to process information categorically as opposed to literally and linearly as with sensors.
For example, highly intuitive people are more likely to use, understand and appreciate metaphor. Metaphor is a non-linear approach to synthesizing information. If I had to choose a defining characteristic of intuition, I would choose metaphor. Some would call intuition the ability to perceive possibilities in the external world or even in internal systems, but sensors do that too. The difference is that intuitive can generate more possibilities faster, but they can't do it in ways that are readily justifiable. Hence metaphor.
Problems with the theory? Well, the theory depends on self-perception of individuals, so if a highly intuitive individual were to view their thought patterns as concrete and step by step as I often do because they are so used to such an irregular mode of synthesizing information, their answers might not match up to how they actually think. I assume the same is possible in reverse, but I'm not sure how.
The theory is a gross oversimplification; we know that. Obviously, there are some people who are very good at gathering information with both S and N functions. These people, who probably constitute a significant portion of the population, may use both kinds of functions to significant degrees, especially if they are highly intelligent. These people are probably the easiest to confuse (not necessarily the intelligent ones). I do believe that some people use S and N functions to an equal degree.