The biggest mistake they made was bringing the wrong set of people to handle the club from Ed Woodwards down to David Moyes, those were wrong choices and I believe Ferguson somehow played a role in their down fall cause he approved the selection of a wrong coach to supersed him cause he's his country man. Another big mistake Manchester United made was sacking Coaches like Jose Mourinho and Ole Gunner Solkjer if only they gave them enough time like Arsenal has given Arteta.
Well they'll continue to be left out of the top 6 if they fail to do the right things, good for them that they've employed the right people at the board level, what's remaining is helping their coach get his right players to carry out his instructions properly then they'll gradually begin to perform well again.
Since Ferguson left the club Manchester United have not been a club recognized with that level of patience with managers. They have been known to be strict and inpatient with managers just like Chelsea believing the managers were the problem why the club has struggled for years to maintain stability in their performance at all levels ignoring the fact that the problem traces up to the top hierarchy too.