No, he was actually the best Batman detective in the movies.

You're focusing only on why Batman didn't figure that Superman is Clark Kent. There are two reasons why. The first is that he had no reason whatsoever to think that Superman was acting as a man. His entire vision of Superman was as a powerful alien time bomb, set to snap and wipe out the world at any time. The second is that his rage over the Battle of Metropolis had him hyper-focused on just killing Superman. That hyper-focus and rage is also what allowed Lex Luthor to manipulate him. Being a great detective doesn't make one all-knowing and it doesn't make one immune to outside manipulation.

Meanwhile, throughout the movie, he used his detective skills to find the White Portuguese and to locate enough kryptonite to accomplish his mission. Compare that to Keaton, Clooney, and Bale, who all did nothing detective-like, or Adam West and Val Kilmer, who could solve riddles.