I don't think Solskjaer has done that bad over the last couple of seasons. He's not top drawer tactically, but frankly, neither was Ferguson, but they're both good man managers, which at a club that spends like Man Utd and therefore for most games fields better players, is often enough.
What has let him down is the signing of Ronaldo. His workrate was always going to have a negative impact and would require some rethinking and teething especially in big games against fully formed teams like Liverpool. Whoever the manager, they're going to have the same problem.
I've read a lot of fans think that the main problem is the lack of top quality defensive midfield. It isn't. The problem is that the squad, from top to bottom is more suited to playing compact, direct, counter attacking football, but in order to transition into a more complete, versatile and consistent team, they have to be able to play with some proper pressing. That pressing was evident at times last season and Ronaldo completely wrecks that. He was possibly the worst signing imaginable. The main problem is that none of the forwards bar Cavani, whilst all scorers of good goals, are good enough do to it either.
I don't believe that Solskjaer would have actively wanted to sign Ronaldo either. He's been offered the chance and taken it, sure, but he most probably didn't have much say in it.