There is a remarkable absence of dirt around the grave in the opening scene. For someone to dig a 6 foot deep hole by hand, there should be more dirt visible near the hole.
When Steve and Danny argue over who's at fault for their restaurant getting robbed, Steve comments that it amazes him that Danny is allowed to carry a firearm, to which Danny retorts that Steve, not the state, is the one who hired him. While it's true that Steve recruited him into Five-0, Danny seems to be forgetting that, until he accepted the offer, he was employed by the Honolulu Police Department.