Do introverts tend to experience more psychological problems?
Several other disorders relate to introversion, including:


Avoidant personality disorder (Morey et al., 2002)
Obsessive-compulsive disorder (Samuels et al., 2000)
Schizotypal personality disorder (Funder, 1997? Don't have it on-hand, but will try to verify this later when I do.)
Schizoid personality disorder (Morey et al., 2002)
Generalized anxiety disorder in young adults (ages 25–39; Kessler et al., 2008)


I would not expect lack of ideas to mediate these relationships. Introversion is sometimes thought to relate to "richer inner worlds" (can't recall where I read that, and I don't put a lot of stock in the claim). Introversion relates negatively to openness to experience, but seems to have a complex relationship with creativity. A common theory about introversion is that it relates to interest in reading (found some such evidence in Chinese adolescents so far; Lau &amp; Cheung, 1988); this would certainly help with any lack of ideas.

References
- Funder, D. C. (1997). The personality puzzle. W. W. Norton &amp; Co.
- Kessler, R. C., Gruber, M., Hettema, J. M., Hwang, I., Sampson, N., &amp; Yonkers, K. A. (2008).  Comorbid major depression and generalized anxiety disorders in the National Comorbidity Survey follow-up.  Psychological Medicine, 38(3), 365–374.
- Lau, S., &amp; Cheung, S. M. (1988). Reading interests of Chinese adolescents: Effects of personal and social factors. International Journal of Psychology, 23(1-6), 695–705.
- Morey, L. C., Gunderson, J. G., Quigley, B. D., Shea, M. T., Skodol, A. E., McGlashan, T. H., ... &amp; Zanarini, M. C. (2002). The representation of borderline, avoidant, obsessive-compulsive, and schizotypal personality disorders by the five-factor model. Journal of Personality Disorders, 16(3), 215–234.
- Samuels, J., Nestadt, G., Bienvenu, O. J., Costa, P. T., Riddle, M. A., Liang, K. Y., ... &amp; Cullen, B. (2000). Personality disorders and normal personality dimensions in obsessive—compulsive disorder. The British Journal of Psychiatry, 177(5), 457–462. Retrieved from http://bjp.rcpsych.org/content/177/5/457.long.