Question

I study in a hesder yeshiva. In the neighborhood there is a rabbi who issues Jewish law rulings, and several times already he has ruled incorrectly, for example on the laws of the Sabbath, prayer, and Passover, and I showed him that it was an explicit mistake and he retracted it.
In my opinion he is an irresponsible rabbi, because these are fairly explicit matters that are easy to find with a search. Sometimes he simply rules from memory and makes a mistake, or he knows a dispute among the medieval authorities but not the later authorities who explained things.
What am I supposed to do in a situation like this? Telling him to be serious does not help. Speaking negatively about him feels problematic, because maybe I am also exaggerating. I am not a great expert in Jewish law, but with today’s books and Google, on simple questions you can reach the sources without much difficulty, and he does not always do that. I thought about reporting him to a major rabbi with examples, but without the name at first.