Other forms: exceptionably
If something is exceptionable, someone is bound to find something wrong with it.
Be careful not to confuse exceptionable with exceptional, which means something remarkable and particularly unusual, or with unexceptionable, which means the exact opposite of exceptionable — something quite ordinary and hardly to be noticed. "Puppies are cute" is about as unexceptionable a sentence as you are likely to find. Unless you're a puppy hater, of course.