For a second incidence of spitting at school then, yes, I'd have a serious talk and some consequences at home. I don't think they're too young to understand that, at four. Spitting is, IMO, in a different league of behaviour to little kids jostling/grabbing/not sharing. It's not a temporary failure of empathy or patience, especially if it happens more than once. It's very aggressive and the spitter's only 'reward' is shock and negative attention. Do you know what prompted this?
I also think you need your DH to seriously rethink his position, because his apparent need to minimize the behaviour is very unfair to your son. He's so little, and all he knows about acceptable behaviour comes from the adults around him. Even if his father never openly shows contempt or disapproval for discipline, children pick up on attitudes and it must be terribly confusing for him, getting completely different ideas about what is okay. You said he talks about his good heart and his bad heart? I know that's not an uncommon idea, with kids, but it also suggests he doesn't feel entirely in control of his behaviour. Again - not rare, with younger kids (especially tired ones who've just started school), but something to pick up on if he's feeling bounced between two very different standards of behaviour (between you and your DH, or home and school).
You say two childminders have quit as a result of his behaviour, and he had constant trouble at nursery, and now trouble from the start at school. He's very young, but it's clear this is a sustained issue, not a series of one-offs. I would think he's beginning to associate education or other care settings with being reprimanded, and this can compound as he gets older. It must be hard for him to develop positive relationships with caregivers. And it's so unfair, because it's obviously not his fault. Your husband needs to work out why it's more important for him to maintain his laid-back approach to discipline when his son's constantly paying the price.
(And by disclipline I don't mean some archaic system of penalties, obviously! More a consistent framework which enables your son to enjoy himself whilst behaving in a way which doesn't earn him constant problems outside the home.)