Actually Golden Age Batman was dark. He killed and even carried a gun for a while. It was the Silver Age that made him goofy. Cactus aliens, rainbow batsuit, Joker's boner. Just plain sillieness
Batman was more campy in the 50s. Julius Schwartz took over in the 60s and actually made the character a lot more serious. Unfortunately the show got so popular that DC forced him to switch the tone again for a few years. Once the shows ratings declined it got more serious again.
Like everyone else has said, it's just over-the-top and campy fun. The show doesn't take itself seriously and it somehow works. I used to rush home from school to watch the episodes back to back, I loved it. Thankfully found the entire show on a bootleg dvd set for relatively cheap recently.
Mad Hatter was a favorite of mine, I'm not even sure why really.