"Err on the side of caution." That's because "err" is a verb. In your sentence, you are saying someone is committing the act of erring. Therefore, "to error" would be incorrect.
Please note: the answer below is a spoof. Continue in your search, or you will sound ignorant to those who know that to err is human. To 'air' is just careless.You would, ideally, pronounce the word...