What is the evidence to suggest that the introvert/extrovert distinction is a shallow distinction?
I think it is safe to say that in psychological research on personality differences, extraversion (vs. introversion) is one of the most important personality dimensions. In fact, extraversion (along with neuroticism) has been included in "virtually all major dispositional models" (see Watson,
Clark, &amp; Harkness, 1994; Zuckerman, Kuhlman, Joireman, &amp; Teta, 1993; as cited in Watson et al. 1999). Extraversion can be reliably measured with personality questionnaires (e.g. Costa &amp; MaCrae, 1992), it is a heritable trait (e.g., Jang et al. 1996) and it meaningfully predicts other important variables such as trait positive affectivity (Watson et al. 2009) or job satisfaction (Judge et al., 2002) to pick two arbitrary examples.

Of course, neither does this mean that it is useful to categorize people into introverts and extraverts (personality research has long moved away from "type" approaches to investigate gradual differences) nor does this mean that extraversion is the only personality difference that matters (it is an important one, but there are others).

In conclusion, extraversion-introversion is a robust and widely replicated personality dimension that features in almost all models of personality.

References

Costa, P.T.,Jr. &amp; McCrae, R.R. (1992). Revised NEO Personality Inventory (NEO-PI-R) and NEO Five-Factor Inventory (NEO-FFI) manual. Odessa, FL: Psychological Assessment Resources.

Jang, K.; Livesley, W. J.; Vemon, P. A. (1996). Heritability of the Big Five Personality Dimensions and Their Facets: A Twin Study. Journal of Personality 64 (3): 577–591.

Judge, T. A., Heller, D., &amp; Mount, M. K. (2002). Five-factor model of personality and job satisfaction: A meta-analysis. Journal of Applied Psychology, 87, 530–541. doi:10.1037/0021-9010.87.3.530

Watson, D., Wiese, D., Vaidya, J., &amp; Tellegen, A. (1999). The two general
activation systems of affect: Structural findings, evolutionary consider-
ations, and psychobiological evidence. Journal of Personality and Social
Psychology, 76, 820–838.