From the treatment of her prisoner,to the shooting of an officer who refused an order,all I see is an ego maniac.
Not professional behavior, though shooting somebody for gross disobedience of orders (in a mutiny way during combat) can be a judgment call. In the implied scenario perhaps not one calling for immediate action.
But then Adama has a crewman who shot the 1st Cylon Susan without orders (showing a lack of discipline and destroying a potential intelligence source) and got a slap on the wrist, the bickering and fraternizeing and lack of military bearing among the crew members, other disobedience not related to the military coup and an XO that is a disaster by any neutral evaluation with know problems and clear examples of questionable judgement.
There might be a reason Adama is outranked by a much younger officer, and maybe its not that he is some misunderstood Billy Mitchell

I can live with that as a creative element, with him being a flawed commander that ultimately does more good than evil.
The biggest potential series problem I see is the “Star Trek Away Team Syndrome,” where all the major characters who shouldn’t be doing silly things end up doing silly things to be part of the story -- like the chief going on missions he shouldn’t be allowed to participate in because he is valuable as a shipboard maintenance resource. I have a really hard "suspension of disbelief" time with that, and it killed the promising Enterprise series for me.
Charon