Your sentence does not use "but" correctly. "But" can be used to emphasize _impossibility_. For example, you can say "one cannot but notice that it is going to rain soon" to emphasize the impossibility of not noticing that it is going to rain soon". A correct way to write your sentence is: "One cannot but commit errors." "One" is much better than "no one" because "no one" needlessly introduces a double negative.

We don't. This sentence is wrong. I think "There is no one who doesn't commit errors." is what the sentence means.