Pilots will make serious mistakes
Although pilot error can cause an accident or serious incident, systems in aviation are generally such that only multiple failures or errors will have a bad outcome. There is a constant process of verifying, cross-checking and so on.
It's true that people, including pilots, make mistakes. But that's only part of the truth; in fact people (including pilots) will make mistakes, as a matter of course. That is what they are expected to do, and that's why the systems they work with are so successful at preventing those mistakes from turning into serious
Accidents tend to represent the failure of systems, not individuals
Accidents tend to happen when the system breaks down and fails to prevent an error developing into a situation. The classic example is AF447, in which a long series of errors (both human and mechanical) occurred; the system that broke down between the three crew members in the cockpit was that of communication.
It would be pretty useless to (say) choose to avoid flying with pilots whose errors had led to accidents. Pilots flying right now all over the world will have made and will be making exactly the same mistakes, just with different outcomes.
It would be better to enquire after patterns
It would be much more useful (but also much more difficult) to know if the systems, patterns and habits at work in the cockpit and beyond were ones conducive to the production and sustenance of uncorrected errors.
For example: the pairing of a laconic and prickly captain with a cowed first officer. Or: an actual practice within an airline that's at variance with standard operating procedures. Or: flight rotas that have left both flight crew with disrupted sleep that week.
The industry's attitude torwards serious error
The aviation industry has an attitude towards mistake-making or even impaired pilots that's quite different from the one expressed in the question.
Each year, quite a number of commercial pilots are arrested for turning up to work (or in some cases, for finishing a shift at the controls) drunk. People might not want to get in a plane with a pilot who'd been previously been arrested for that, but the industry (actually I only know about cases from the USA, so I'd be interested to know more about other regions) has different ideas.
In fact many of them eventually return to work. In the USA the HIMS programme is key to this.
For example, Lyle Prouse, an alcoholic Northwest Airlines captain, served a 16th month prison sentence after being convicted of flying influence of alcohol in 1990. Three years later he was flying again with the same company, and retired in 1998 as the captain of a 747.