All of this depends on the jurisdiction, but most western countries have some kind of defense for corporations making mistakes

Usually it's something like "if the offer is clearly a mistake, you don't have to honor the sale", but rental agreements are a bit of a grey area, since they are a contract between two individuals instead of a sale

I'd say go for it, but be prepared to be sued

Depends on where you are. In my city, yes, technically if they didn't give me any notice that the rent was changing and the lease said that then I would be legally allowed to live rent free until they gave me notice, and the time required to give me notice would depend on how long I lived there. Rent stuff is always a huge huge "it depends." Even if the law was on your side they would probably sue you for the back rent and then you'd have to go to court or automatically lose. And even then I could see plenty of asshole judges going "clearly they didn't mean that" and ruling in their favor anyway.

My guess is a judge would view the typo based on intended meaning. You can defijirely get away with paying the same rent as before the lease expiry, but paying nothing may be a dangerous game.

Your previous contract, executed and signed by you or your legal representative, almost certainly includes a clause on what happens in the “month-to-month” scenario. This clause almost certainly does not state $0.

The renewal letter has not been signed and executed by both parties.

I’m all for fucking over landlords, but we also need to pick our battles 😁

If you want to roll the dice because you don't have anything to lose, I'd put your current rent amount away in a savings account that you don't touch.

If they take it to court or some shit, you can probably make a decent case for why it's unfair for them to increase the rent without providing you notification so you owe them your current rent amount for however long it took before they amended the error.

Or just run on no rent and bail when shit gets serious. This may have implications for getting future tenancy.

Idk. I'm not a lawyer but you have the chance to push your luck at least a little bit and as long as you keep your head on your shoulders about it, you might come off in a better position than you otherwise would.

As everyone else says, probably not, but it depends on where you are: if you want a real answer, you're going to have to ask a local lawyer. Unless you're confident you can shoulder the potential costs (or otherwise be immune to them) it's probably not worth trying.