The thing about true competency isn't that fuck-ups never happen, it's how you deal with fuck-ups when they do.
In TNG the crew are generally capable, professional, and most importantly pull in the same direction. When a problem happens they put their heads together and solve it without ego.
Compare to other (also good) space shows like Battlestar Galactica, where almost the entire plot is driven by secret identities, hidden agendas, backstabbing, and personal drama.
TNG is competency porn because while Individuals are flawed, the crew as a whole are together brilliantly capable.