George Graham said in an interview the key to management is to not achieve anything that you can not repeat. That is the sin Moyes has committed in so many peoples eyes, Champions league football and finishing above Liverpool. This was never going to be something that was regularly achieved at Everton, and for that reason Moyes suffers the fate GG said you should never get yourself in. Moyes is the best thing to happen to Everton for a long time, the fact the supporters have to be above the madding crowd, is the cost of overachieving.
There are 3 concepts managers are judged by. Tactical ability, this one is a complete myth, fans of any club now or from the past always argue about team selection and substitutions. There are no great tactical managers[ The tulip revolution guy might be and the Hungarian 4 3 3 and German sweeper system] Chelsea, Man Utd and Arsenal fans question the manager and think he should have done X over Y. That is the game, managers make decisions when they come off they are great when not they are crap.
Motivating the players; Getting the most out of the players the manager has, Moyes is at least a 9 out of 10 at that, he has got great performances out of average players again and again.
Buying players; After Wenger Moyes record in the transfer market is the second best, he has bought countless players at miles bellow their real value. His record in the transfer market is fantastic. He has made mistakes, but there is a fantastic buy to balance it out. Moyes has a great transfer record, those that dislike him can not accept it, but he is miles in the black on transfers and there are very few manager who can say that.