You are describing the actual malice standard which only applies to public figures. Also, an accusation of that type would be considered "defamation per se" which would mean that there is not a need to prove damages. According to my layman understanding.
am I also fine if I negligently write and keep using an algorithm to detect and report people for being molesters when I know full well that it's actually shitty and I regularly receive reports that it's resulting in false positives?
That's facebook's situation. Even though they've got hundreds of billions and could easily afford to, they don't want to pay humans to verify these things and they know that innocent people are being hurt by their terrible lazy code, they just don't care.
I suppose you'd have to prove that they knew the algorithm was bad. They'll just say "we're trying our best, but it's hard". And the truth is that it probably is hard. The question is whether knowing that your algorithm is imperfect is equivalent to intent to harm.
Sure there is, they're a bigcorp and did what they did. Don't let companies get away with crimes you and I wouldn't just because they're too disorganized.