Crossword puzzle clue "bit as of sense"

"No sense is so uncommon as common sense"?

"The Sixth Sense" sense

Bit of horse sense?

Bit, as of sense

Bit player whose casting as Dr. Hill in "The Sixth Sense" was hardly a surprise twist since he was pretty much always on the set

Bit of Web clutter, and a hint to making sense of four answers in this puzzle

It bit in a Shakespearean bit

Took away bit by bit