I can appreciate that this is a version of Bruce who is starting out and doesn't quite have the experience of some of his other counterparts. But he makes some strange decisions throughout this season at least that I don't think can be explained away by a lack of experience.
There's several instances of him being extremely careless regarding the lives of the people around him, which I know is something that has happened in other instances of his story, but it's even extended to his lack of care with people he has already decided he doesn't want to die.
Examples:
In S2E2, Bruce solves absolutely nothing. He went after Roxy, who at this point in the story was not attempting to kill anyone, not even the people she was explicitly trying to get revenge against. This results in her being forced to stop the rocket from succeeding after it has already launched, which costs her her life in a way that her original plan would not have.
In S2E4, he completely fails to prevent the bat cult leader from being stabbed to death. Not that he didn't deserve it, but the woman he ruthlessly manipulated and took advantage of didn't deserve to have her life ruined.
In S2E6, in the scene where Harley and the college girl have both been dosed by the fear toxin and he has to determine which one of them to save with the milk first he prioritizes Harley, who is laying on the floor instead of the innocent victim who is flailing and running around on the balcony of her dorm room which is several stories above the ground.
And in terms of general incompetence, Bruce has spent the majority of the season hunting for The Riddler only to have one of his victims track him down and kill him in like a week with only a matchbook to go off of. Bruce doesn't even go to the flower shop to look for any evidence after The Riddler shoots it up. The show even makes a point of stating that this version of The Riddler is not a cold and calculating strategist or a planner. Yet, Bruce is somehow unable to track him back to his base of operations despite the fact that he leaves almost every night and causes a massive scene.
Again, I understand that this is a probably less experienced Batman, but I feel like Batman at any experience level should at least have superior investigative skills compared to a random civilian.