What exactly has LVG done wrong?
Lots of things. He's done lots of things right, of course, but off hand, mistakes so far:
Player Personnel
1. Rafael frozen out and not given a chance.
2. Herrera not a starter for months, which was just flat out wrong.
3. Falcao, over and over upfront. Why?
4. Di Maria, coming off being the CL MOTM, hasn't been able to help us. Realistically, if we were going to challenge for the title, he would have had too.
5. Rooney not as a 9 and instead playing in midfield. See #3, here.
6. There are reports he hasn't gotten on with De Gea that well. That won't help us retain him.
General
7. 3 at the back didn't really work, all in all, and it was what he implement after having much of the window, lots of money and some decent players already in the squad to work with.
8. We've got 7 points in our last 6 games, so tough to argue we're ending the season with great momentum.
9. We've looked coherent and solid with this 4-5-1 most of the time, but also very predictable.
10. Our buildup is so slow that we seem to need Fellaini out there to generate offense and that sort of thing has a limited upside. We aren't challenging for the title year in year out and consistently getting to the semis in the Cl with that.
Klopp wouldn't be perfect, but Van Gaal isn't either.
I do think Klopp would fit out personnel better in that he'd be comfortable playing 4-2-3-1 with Rooney up top, Mata as a 10, Di Maria and Memphis on the wings and Herrera and a more defensive partner like Carrick or Blind. But I also think that team would be a bit haphazard and we might concede more.
Klopp may be available in 2-4 years when Van Gaal likely goes. Managers don't stick anywhere too long, and Van Gaal seems likely to be able to keep us in the CL and Woodward and the money people are consistently signing players in their early 20's who are going to improve and are already good enough like Herrera, Shaw and Memphis, so I don't think we'll be worse off staying with Van Gaal for another few years and letting him fix the team before the next manager gets the spoils, like Heynckes did at Bayern.