Accumulation of asks. Asking for a single thing like early check-in is no problem. I start seeing orange and then red when its multiple things: they ask for early check in, late check-out, use of non-listed amenities like washer dryer, baggage storage, receiving mail at my address, or they want to bring their "perfectly behaved pet" when I'm a "no pets" place.
Any ask to go off-platform is an immediate no.
Locals or people moving to the area: Sometimes locals book for a party/event location. Sometimes they're legit between leases for a few days, but sometimes there's good reason they can't find housing. Be sure they aren't booking for a length of time that might give them tenants' rights
Third party. Most of these are innocent, like an adult child booking for parents, but I always ask them to re-book under their own account. Almost without fail, if I accept a 3rd party booking the communication becomes a nightmare because Airbnb messages don't get to the correct person and you'll either get no review, or one left by the booking person who never set foot in your place.
A red flag for most hosts that's worked out fine for me: wedding, bachelor, or bacheorette groups. If I had a whole house rental where I wasn't on property, I'd be more wary of these groups, but I've hosted dozens with only one issue (the vomit queen of 2018).