Our justice system is not perfect and innocent people can be wrongly accused, prosecuted or even convicted. Miscarriages of justice and wrongful allegations are not as rare as you might think.
The University of Exeter Law School has been building a register of miscarriages of justice. On their site you can read about each case. There are also useful Wikis about the issues causing miscarriages of justice. The site describes the four main issues. These are failures of disclosure, false confessions, unreliable witness evidence and unreliable forensic evidence.