Personally, I'd further qualify that. It should be logged as an error if the person who reads the logs would be responsible for fixing it.
Suppose you run a photo gallery web site. If a user uploads a corrupt JPEG, and the server detects that it's corrupt and rejects it, then someone needs to do something, but from the point of view of the person who runs the web site, the web site behaved correctly. It can't control whether people's JPEGs are corrupt. So this shouldn't be categorized as an error in the server logs.
But if you let users upload a batch of JPEG files (say a ZIP file full of them), you might produce a log file for the user to view. And in that log file, it's appropriate to categorize it as an error.
4xx is for client side errors, 5xx is for server side errors.
For your situation you'd respond with an HTTP 400 "Bad Request" and not an HTTP 500 "Internal Server Error" because the problem was with the request not with the server.
You cannot accurately assign responsibility until you understand the problem.
Some of these things can be ameliorated with well-behaved UI code, but a lot cannot, and if your primary product is the API, then you're just going to have scads of ERRORs to triage where there's literally nothing you can do.
I'd argue that anything that starts with a 4 is an INFO, and if you really wanted to be through, you could set up an alert on the frequency of these errors to help you identify if there's a broad problem.
In other words, of course you don't alert on errors which are likely somebody else's problem. You put them in the log stream where that makes sense and can be treated accordingly.
- An error is an event that someone should act on. Not necessarily you. But if it's not an event that ever needs the attention of a person then the severity is less than an error.
Examples: Invalid credentials. HTTP 404 - Not Found, HTTP 403 Forbidden, (all of the HTTP 400s, by definition)
It's not my problem as a site owner if one of my users entered the wrong URL or typed their password wrong, but it's somebody's problem.
A warning is something that A) a person would likely want to know and B) wouldn't necessarily need to act on
INFO is for something a person would likely want to know and unlikely needs action
DEBUG is for something likely to be helpful
TRACE is for just about anything that happens
EMERG/CRIT are for significant errors of immediate impact
PANIC the sky is falling, I hope you have good running shoes