Non-reversible or 'persistent' side effect incidence rates have not yet been established, but it's estimated that it's extremely rare, probably in the range of 1/500 or 1/1000. No one really knows how common it is, or to what extent (severity) a person will be affected. There is also no information about persistence; some people have reported that the side effects abate over time, some say that they get worse. It's all really anecdotal right now, and there's no real way to measure any of this. There is a risk with taking finasteride, but it's extremely low, and you probably partake in much riskier activities on a daily basis.
Roughly 5% of users will have side effects initially (one or more of erectile dysfunction, decreased libido or ejaculation disorder) and after 5 years of continued use, side effects are almost non-existent meaning that they will abate over time.