BPA is a well-known endocrine disruptor. In some cases it acts like a hormone (ex: estrogen) in some cases it blocks hormones. The dangers of BPA include how common it is, multiple effects in the body, and long-lasting effects. Effects continue even after exposure stops. Most studies listed here control for various variables likes sex and age. Here is a list of studies by system, showing the effects of BPA.
It is my intention to update this as I get more information, and use this as a central source of studies by system. If you have a study to add, please cite it in the comments and don't forget to add a plain text link. I will format the study and add it to this page.
Breast CancerMordukhovich I, Beyea J, Herring AH, Hatch M, Stellman SD, Teitelbaum SL, Richardson DB, Millikan RC, Engel LS, Shantakumar S, Steck SE, Neugut AI, Rossner P Jr., Santella RM, Gammon MD. 2016. Vehicular traffic-related polycyclic aromatic hydrocarbon exposure and breast cancer incidence: the Long Island Breast Cancer Study Project (LIBCSP). Environ Health Perspect 124:30-38; http://dx.doi.org/10.1289/ehp.1307736.
Nudelman, Janet, MA. State of the Evidence: The Connection Between Breast Cancer and the Environment 2010. Breast Cancer Fund. 2010. 132 pgs.
Shankar A, Teppala S. Relationship between Urinary Bisphenol A Levels and Diabetes Mellitus. The Journal of Clinical Endocrinology and Metabolism. 2011;96(12):3822-3826. doi:10.1210/jc.2011-1682. Results: Positive correlation between urine BPA levels and diabetes.
Heart DiseaseMelzer, David, et al. Association of Urinary Bisphenol A Concentration with Heart Disease: Evidence from NHANES 2003/06. Jan 2011, plos.org. Results: higher urine BPA levels associated with higher rates of various types of heart disease. (See table on study for types of heart disease.)
Slomski A. Chronic Mental Health Issues in Children Now Loom Larger Than Physical Problems. JAMA. 2012;308(3):223-225. doi:10.1001/jama.2012.6951. Results: Top 5 issues for kids are now mental health issues. This article simply points to: http://futureofchildren.org/futureofchildren/publications/article-summaries/22-01/.
Multiple problems studied
Reducing Environmental Cancer Risk. 2008-2009 President's Cancer Panel Report. 240pgs. PDF. "About 41% of Americans will be diagnosed with cancer in their lives, about 21% will die from it."