Supervised Learning could be biased if we use obsolete data What if the data that we could use for the training is obsolete. For instance, if I train my model with the computer sales report from the 20th century and try to predict the actual trends, a disaster, right?

Another good example is the one that profiles criminals. It will use the historical "mistakes" as fact and could wrongly suspect innocents(based on race or ethnicity).

How could I avoid this kind of situations?
One approach to using knowledge from the example you gave above is to use that information as a prior for your current model. While it is unlikely that the exact trends observed a while ago will predict future trends, some general observations/correlations will likely still be relevant for the present day. 

Concerning your example of criminal profiling. Making predictive models in such cases can be highly biased and is controversial. I invite you to read the Outlook section XVIII.D of this ML review on the social implications of machine learning and the references mentioned.