Prevalence of psychological "problems" Giulio Cesare Giacobbe is an expert of psychosynthesis. In one of his books (Alla Ricerca delle Coccole Perdute) he speaks of childish, neurotic people. He says most people are childish and neurotic.

Dale Carnegie explains in his book How to Win Friends and Influence People that people are often cocky, narcissistic and so on.

Wayne Dyer writes in his book Your Erroneous Zones that the instruction system creates distortion and problems in persons.

One statistic described 3.5% of people experiencing psychological dystonic problems (anxiety, OCD, etc.). I would guess that the number or people experiencing bad thinking, cognitive distortion, and other strong, dysfunctional personality traits could be very high. Are there any statistics on that?
Not entirely sure what specific stats you'd be interested in, but Wikipedia has plenty on prevalences of specific mental disorders. For anxiety disorders, which include obsessive compulsive disorder:


  A review that pooled surveys in different countries up to 2004 found overall average prevalence estimates for any anxiety disorder of 10.6% (in the 12 months prior to assessment) and 16.6% (in lifetime prior to assessment), but that rates for individual disorders varied widely. Women had generally higher prevalence rates than men, but the magnitude of the difference varied [(Somers, Goldner, Waraich, &amp; Hsu, 2006); emphasis added].


However, Wikipedia's section on epidemiology of anxiety disorders page gives different numbers:


  Globally as of 2010 approximately 273 million (4.5% of the population) had an anxiety disorder [(Vos et al., 2013)]. It is more common in females (5.2%) than males (2.8%). In Europe, Africa and Asia, lifetime rates of anxiety disorders are between 9 and 16%, and yearly rates are between 4 and 7% [(Simpson, Neria,  &amp; Lewis-Fernández, 2010)]. In the United States, the lifetime prevalence of anxiety disorders is about 29% [(Kessler et al., 2005)] and between 11 and 18% of adults have the condition in a given year. [Emphasis added.]


For OCD specifically: 


  OCD occurs in between 1 to 3% of children and adults [(Sarvet, 2013)]. It occurs equally in both sexes...A 2000 study by the World Health Organization found some variety in prevalence and incidence of OCD around the world, with figures in Latin America, Africa, and Europe at two to three times those in Asia and Oceania [(Ayuso-Mateos, 2000); emphasis added].


Here's a cool figure of "age-standardized disability-adjusted life year rates from OCD by country (per 100,000 inhabitants)" uploaded to Wikipedia by Lokal_Profil (darker $&gt;$ lighter; click for the scale):



"Bad thinking, cognitive distortion, and other strong, dysfunctional personality traits" is a little too vague to work with much further, but here's Wikipedia's info on prevalence of personality disorders in general:


  Studies of the prevalence of personality disorders (PDs) have been fewer and smaller-scale, but a broader Norwegian survey found a similar overall prevalence of almost 1 in 7 (13.4%), based on meeting personality criteria over the prior five-year period. Rates for specific disorders ranged from 0.8% to 2.8%, with rates differing across countries, and by gender, educational level and other factors [(Torgersen, Kringlen, &amp; Cramer, 2001)]. A US survey that incidentally screened for personality disorder found an overall rate of 14.79% [(Grant et al., 2004); emphasis added].


Finally, neuroticism is a continuous dimension of individual differences with an approximately normal distribution. As such it is largely defined in terms of degree relative to population norms, and it doesn't make much sense to say "most people are childish and neurotic." (That is, I imagine we'd want to define "childish" in a similar way if we wanted to make any objective statements about population levels.) I'm unaware of any ratio-scaled measures of neuroticism (and find it hard to imagine any that wouldn't be very controversial), so as an interval-scaled construct at best, there is no meaningful "zero neuroticism". Hence, depending on what it means to you, you could either say:


"Everyone's a little bit neurotic (at least)!" or, 
"$\approx49.\bar{9}\%$ of the population is neurotic, and the same proportion are not."


Statement 1 would be Giacobbe's best defense, but that's not saying much – nor does the statement as I've phrased it, though it's an improvement. A better interpretation of his statement (at least, as you've phrased it) would probably be as the subjective opinion, "I find most people to be childish and neurotic [compared to myself, or compared to how I would expect them to act due to other factors, which I'm probably ignoring]."

References


- Ayuso-Mateos, J. L. (2000). Global burden of obsessive-compulsive disorder in the year 2000. World Health Organization. Global program on evidence of health policy, global burden of disease. Retrieved from http://www.who.int/healthinfo/statistics/bod_obsessivecompulsive.pdf.
- Grant, B. F., Hasin, D. S., Stinson, F. S., Dawson, D. A., Chou, S. P., Ruan, W., &amp; Pickering, R. P. (2004). Prevalence, correlates, and disability of personality disorders in the United States: Results from the National Epidemiologic Survey on Alcohol and Related Conditions. Journal of Clinical Psychiatry, 65(7), 948–958.
- Kessler, R. C., Berglund, P., Demler, O., Jin, R., Merikangas, K. R., &amp; Walters, E. E. (2005). Lifetime prevalence and age-of-onset distributions of DSM-IV disorders in the National Comorbidity Survey Replication. Archives of General Psychiatry, 62(6), 593–602. Retrieved from http://www.ph.ucla.edu/epi/faculty/detels/PH150/Kessler_DSMIV_AGP2009.pdf.
- Sarvet, B. (2013). Childhood obsessive-compulsive disorder. Pediatrics in Review, 34(1), 19–28.
- Simpson, H. B., Neria, Y., &amp; Lewis-Fernández, R. (Eds., 2010). Anxiety disorders: Theory, research and clinical perspectives. Cambridge University Press.
- Somers, J. M., Goldner, E. M., Waraich, P., &amp; Hsu, L. (2006). Prevalence and incidence studies of anxiety disorders: A systematic review of the literature. Canadian Journal of Psychiatry, 51(2), 100–113. Retrieved from http://ww1.cpa-apc.org/Publications/Archives/CJP/2006/february/sommers-RP.asp.
- Torgersen, S., Kringlen, E., &amp; Cramer, V. (2001). The prevalence of personality disorders in a community sample. Archives of General Psychiatry, 58(6), 590–596.
- Vos, T., Flaxman, A. D., Naghavi, M., Lozano, R., Michaud, C., Ezzati, M., ... &amp; Brooker, S. (2013). Years lived with disability (YLDs) for 1160 sequelae of 289 diseases and injuries 1990–2010: A systematic analysis for the Global Burden of Disease Study 2010. The Lancet, 380(9859), 2163–2196.