Hi,
I would like to highlight a problem we encountered while implementing the 404 tracking script on a Wordpress website - without plugin and via js code snippet.
The documentation suggests to use the DOMContentLoaded event to listen to:

<script type="text/javascript">
    document.addEventListener("DOMContentLoaded", () => pirschNotFound());
</script>

but the error we had was:
Reference Error: pirschNotFound is not defined

From the MDN docs:

The load event is fired when the whole page has loaded, including all dependent resources such as stylesheets, scripts, iframes, and images. This is in contrast to DOMContentLoaded, which is fired as soon as the page DOM has been loaded, without waiting for resources to finish loading.

After switching from DOMContentLoaded to load your script have been working properly.
As the pirsch-extended.js library gets loaded via deferattribute I kindly suggest you to update your documentation in order to let others avoid this problem :)

It does not wait for the event request to be completed.

"referrer" : "Referer header (optional)",

in the last code example here https://docs.pirsch.io/get-started/backend-integration/, spells referer instead of referrer 🙂