What are these 'grounds for being wary'?
All I see is he got rid of a failing manager and coaching staff (who would've been kept on by Kenwright, who made a very bad deal and had these people under lengthy deals and would not have been able to afford to pay them off like Moshiri did), who it has since been revealed let the players do whatever the hell they liked and there was no discipline at the club. He brought in a quality manager and coaching staff with high standards and disciplines and more than a plan A & B to win a game.
He's overseen the biggest revamp at Goodison Park in 23 years since the Park End was built, spending actual money to do up the ground.
He's quite clearly driving the new stadium agenda, after years of failure and inertia. He's got the club back on board with the council. He and the rest of the entire board very publicly visited what is quite clearly the forerunner in terms of new stadium sites, a site that will generally please virtually every Everton fan if it comes off. It can't be that far away if the entire club board are pulled from all parts of the country/world, along with an American stadium architect, to visit said site along with the Mayor of the city.
I see nothing to be 'wary' about. There lots and lots of other rich people who buy into football clubs and do virtually nothing, and certainly not as much as Moshiri has done in his first 9 months.