1 a: a question raised for inquiry, consideration, or solution b: a proposition in mathematics or physics stating something to be done;
2 a: an intricate unsettled question b: a source of perplexity, distress, or vexation c: difficulty in understanding or accepting.
The Madoff pyramid scheme is an excellent example of how the same thing at different times can be considered, first, as a solution, and, later, as a problem. In 2004, the Securities and Exchange Comission had information about irregularities at Madoff's firm, but at the time the scheme was supposedly making money for its investors, so nobody bothered to investigate. In other words, it was not a problem then. But in 2008, the exactly same financial arrangement became a problem when people decided to treat it as such. The result of this sudden change of heart?
Obviously, out ability to detect problems is rather limited, even when it concerns vast amounts of money and involves a government agency dedicated to the task. Moreover, having a powerful agency that thinks that something is not a problem is a big problem in itself. One of the ways to deal with it would be to stimulate the public's perception that huge mistakes by government agencies are inevitable and transparency of information flows is essential in detecting such mistakes.
From an inventor/innovator perspective, developing a bank of problems, e.g. by running periodic reverse brainstorms, and monitoring the change in people's perception would be an effective strategy for determining the timing of a product or service introduction.