In addition to these failures, Reconstruction failed to bring the United States together. For decades after Reconstruction, the South continued to be separate from the rest of the US in terms of its politics. Reconstruction was supposed to reunite the country but it clearly failed to do so.
The largest political failure of Reconstruction was to provide suitable enforcement of rights for African Americans. They were freed by the 13th Amendment, made citizens by the 14th; and given the right to vote by the 15th; yet Southern states violated rights with abandon. Former slaves were denied the right to vote for many years by poll taxes, literacy tests (which were often unfairly administered) etc.; separate facilities were the order of the day under Black Codes and Jim Crow Laws which attempted to keep blacks as near slavery as possible; the Supreme Court actually sanctioned this in Plessy vs. Ferguson. Finally, the Ku Klux Klan ran rampant through the South. Reconstruction was never completed; rather the federal government abandoned all attempts at reconstruction by the time Rutherford Hayes was elected President.
While the policies of Reconstruction did successfully convince southern states to apply for readmission to the Union, and provide a legal process to do so (The 10% Plan), and the Constitution was successfully amended to finally settle the issue of slavery, make blacks legal citizens, and grant black males the right to vote, there was no significant reaction from the northern government to southern states continued mistreatment of the freed slaves, and their obviously unconstitutional laws (The Black Codes).
So while political equality and rights were given to freed slaves, it was not enforced, and this is where the main political failure took place.
Another political failure was the refusal of northern politicians to invest funds in the economic and physical reconstruction of the South, such that their economy remained damaged for generations, and the hatred the South felt for the Union was reinforced by that negligence.