Ahhh the shifts debate

I love this one. Ultimately, Riker lodges his & the other dept heads' vague warning about "personnel problems" without having the full scope of understanding of the entirety of what the Captain's goal/plan/mission was (which he is under no obligation to provide)
Therefore, their assessment of what constitutes a significant personnel problem is contingent on a bigger picture Riker is not privy to, given that he is not the man with the entire mission layout.
Given how well informed the captain demonstrates himself to be about everything, right down to where his quarters are & Geordi's engine specs, it's fair to consider that he already
knew exactly what problems Riker was referring to, and had already factored them, especially since he's planning to reassign a whole bunch of other folks anyhow. Riker could be telling him yesterday's news & never even know it.
It's even entirely possible that Jellico only asked Riker what shift rotation they currently had out of politeness, having already known the answer, & already knowing it would need changing, but was trying to at least be diplomatic & conversational about it, as he'd maybe know it potentially represents something objectionable. (He understands no one should be pleased about this change of command)
This is literally his 1st order as captain, & it is not followed though on, because Riker believes himself to have the latitude to delay or postpone or renegotiate it later. He was wrong... & it's not a good 1st impression, & it might have even been a sampler from Jellico, just to test those waters. Fail... which is why despite his look toward him, Picard has nothing to say about it. It's a fail, by any metric.
Edit: the correct procedure would've been to carry out the order. Note the objections, log the concerns, & initiate the directive, problems & all. Then later, if/when those problems arise, bring that to the captain, or earlier if you expect them... but no one's lives were in imminent danger by changing their watch shift, at that time, such that the captain's order should've been ignored, like he was derelict in his duties for ordering it. His call stands.