Liverpool have been having 'disappointing' seasons for a long time now. I am honestly surprised that they seem to have underestimated the effect that Gerrard leaving would have on the whole club. I'm not really a Gerrard fan but IMO he was more than 'just' a captain, and I'm sure the dressing room is a different place without him. Maybe a new manager is the answer to this problem, but maybe not.
Moyes is a bit of a ditherer when it comes to buying players. Which was fine when he was at clubs with little money to spend, you do have to be more careful, but United was different.
Although I think he was screwed either way, if he'd gone in and signed loads of players he would have been criticised. Signing not enough, and he was sacked (amongst other things, but I think that was the beginning of the end).
I agree with you about motivating players. I think one of the issues that many managers have in the Premier league is that these players are on such huge salaries, that they seem to have little respect for the manager, like they are less dispensable than the manager. And they are frequently proved right.