Here are some not uncommon mistakes in reasoning about causation.
Post hoc fallacy - Inferring that X causes Y just because X is followed by Y. Example: "Last time I wore these red pants I got hit by a car. It must be because they bring bad luck."
Mistaking correlation as causation - "Whenever I take this pill my cough clears up within a week, so this pill is very effective in curing coughs." But perhaps mild coughs go away eventually even without taking medicine?
Reversing causal direction - Assuming that X causes Y without considering the possibility that Y is the cause of X - "Children who like violent video games are more likely to show violent behavior. This must be because they are copying the games." But can it be that children who are more prone to violence are more fond of such video games?
Genetic fallacy - Thinking that if some item X is associated with a source with a certain property, then X must have the same property as well. But of course this might not be the case. Example: "Eugenics was practised by the Nazis so it is obviously disgusting and unacceptable."
Fallacy of the single cause - Wrongly presupposing that an event has a single cause when there are many causally relevant factors involved. This is a fallacy where causal interactions are being over-simplified. For example, after tragedy such as a student committing suicide, people and the news media might start looking for "the cause", and blame it on either the parents, the amount of school work, the society, etc. But there need not be a single cause that led to the suicide. Many factors might be at work.
Confusing good causal consequences with reasons for belief - Thinking that a claim C must be true because believing in C brings about some benefit. Example: "God exists because after I have become a believer I am a lot happier and is now a better person."