I think it's best to talk to your host so they can take a look at the logs.
The 404 seems to come from Joomla itself but your template hides all useful information which would help us get an idea of what may be going wrong. Most likely your visitor's browsers are running some extensions which adds something to the request which confuses or browser, or the screenshot they are sending you is missing critical information (they were doing something which submits a form, not just type your site's URL in the browser and hit ENTER).
The only way to find out what happened is to look at the access log for the 404 responses and find out how your users ended up there. If it's POST request, they were submitting a form. Try all controls throughout the site or try to get more information from the visitors to find out what they were doing when they got the error message. If it's a GET request try to see if the visitors are using any browser extensions and whether their IP address is blocked on your server.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!