Information asymmetry is the term for markets that don't work because proper information is not available to both parties - e.g. the broadband speed example that Robert gives.
Adverse selection is a related problem which causes credit to be mispriced. It works like this: companies know more about their business prospects than banks, thus banks will charge a premium on loans to account for the risk they run. This premium puts off creditworthy businesses, whose owners will prefer to invest their own money or raise it in the markets. This leaves only businesses which are middling or downright bad risks still willing to borrow. As the best businesses have left the market, this affects the average risk profile for the banks, who put the rates up again... discouraging the borderline cases and leaving only the really bad risks. Rates then go up again, and... you can see where this leads. This is classically called "the market for lemons" and can lead to a whole market ceasing to operate properly.
Cognitive biases are the specific aspects of psychology where we depart from making rational choices in a predictable way.