This is difficult.
I think we should;
Return 4xx errors only when the client has the power to make a change to the request, headers or body, that will result in the request succeeding with the same intent.
Return error range codes when the expected mutation has not occured, i.e. a DELETE didn't happen or a PUT didn't change anything. However, a POST is more interesting because the spec says it should be used to either create resources at a new location, or just process a payload.
Using the example in Vish's answer, if the request intends to add employee Priya to a department Marketing but Priya wasn't found or her account is archived, then this is an application error.
The request worked fine, it got to your application rules, the client did everything properly, the ETags matched etc. etc.
Because we're using HTTP we must respond based on the effect of the request on the state of the resource. And that depends on your API design.
Perhaps you designed this.
PUT { updated members list } /marketing/members
Returning a success code would indicate that the "replacement" of the resource worked; a GET on the resource would reflect your changes, but it wouldn't.
So now you have to choose a suitable negative HTTP code, and that's the tricky part, since the codes are strongly intended for the HTTP protocol, not your application.
When I read the official HTTP codes, these two look suitable.
The 409 (Conflict) status code indicates that the request could not be completed due to a conflict with the current state of the target resource. This code is used in situations where the user might be able to resolve the conflict and resubmit the request. The server SHOULD generate a payload that includes enough information for a user to recognize the source of the conflict.
And
The 500 (Internal Server Error) status code indicates that the server encountered an unexpected condition that prevented it from fulfilling the request.
Though we've traditionally considered the 500 to be like an unhandled exception :-/
I don't think its unreasonable to invent your own status code so long as its consistently applied and designed.
This design is easier to deal with.
PUT { membership add command } /accounts/groups/memberships/instructions/1739119
Then you could design your API to always succeed in creating the instruction, it returns 201 Created and a Location header and any problems with the instruction are held within that new resource.
A POST is more like that last PUT to a new location. A POST allows for any kind of server processing of a message, which opens up designs that say something like "The action successfully failed."
Probably you already wrote an API that does this, a website. You POST the payment form and it was successfully rejected because the credit card number was wrong.
With a POST, whether you return 200 or 201 along with your rejection message depends on whether a new resource was created and is available to GET at another location, or not.
With that all said, I'd be inclined to design APIs that need fewer PUTs, perhaps just updating data fields, and actions and stuff that invokes rules and processing or just have a higher chance of expected failures, can be designed to POST an instruction form.