People are reading too much passive aggressive intent in Riker's behavior I think. Riker is trying to adjust to a captain with a radically different command style. This takes time. Jellico is expecting Riker to read his mind practically. Riker and Picard have worked together for years. Riker knows how Picard wants things done. Picard knows that he doesn't need to babysit Riker.
If you'll remember in Encounter at Farpoint, Picard did follow up with Riker to make sure his message to the Hood was sent. He didn't have to continue doing that with Riker because after they worked together for a while Picard knew he could count on Riker to get things done without having to babysit him.
Riker is not out of line for wanting to discuss the shift rotation with Jellico after the department heads expressed their concerns. Riker is taking their concerns up the chain of command like he's supposed to. He is trying to make sure that all the information is presented to Jellico.
Jellico is an oppressive, tyrannical asshole with little people skills and a closed mind. I served in the military myself and if I had a commanding officer like that, he would have heard from me too. In fact, I've done it before. I had a first sergeant who stepped way out of line by telling a young soldier who had a different faith that he "needed to be saved." When the other young soldiers saw our first sergeant getting away with it, they started persecuting this kid too. It was wrong. I knew it was wrong so I reminded him his behavior was inappropriate.
My point is officers like Jellico get away with being tyrants because no one challenges them. Yes, there is a right and wrong time for this, but it is still important that lower ranking people remain unafraid to use their voice.