It might be worth asking {The Ladder} for a better idea of Captain Martin's dealings. Then again, I think Lilly could just openly ask him when it comes up-the Spirit fight in the camp might make keeping other secrets seem pointless. Maybe.
Yeah, it's worth wondering if the Ministry of Finance has auditors looking for suspicious activity. The Silas family may or may not be in the clear, depending on how thorough Lord Waters is being, or how much influence he has on them. They also just might not have enough wealth to be noticed in any meaningful way, especially if Yolun was in the habit of trading favors like with the Lye family.
It wouldn't surprise me if Diviners being flighty is becoming more common. Captain Martin mentioned prices were up and accuracy was down, so moving around in search of better fortunes shouldn't be too suspicious.
Captain Martin's case is the most uncertain, because we aren't certain how much pull he has outside of Harmuph. We know he has wealth, at least compared to the Silas family, but it's implied to be far from unlimited.
All 3 moving at the same time, so soon after the wolf attack, might raise eyebrows. But barring Lord Waters' influence, I think the overall level of suspension should be moderate at worst. {The Ladder} implies that Captain Martin thinks his current status is relatively mediocre, and Harmuph isn't the capital of Narisell or anything. We'll have to see.