Since the errors you mention are on a remote server, Id try to test that server as much as possible.
I'd try to discard a problem with my endpoint, which includes my ISP, my browser, firewall and proxy. After that, I'd try to test the other endpoint.
First, try to look for a pattern on the error logs, try to find if it happens because to many connection in a short time, requests from s specific location, old browser, specific version of browser, etc.
Too many connections on a short time period
This should not be a problem for Google servers, but it may indicate a strange situation and some requests may not be getting the normal or complete HTTP response. You can not really test for this, but you can try to detect it and react.
Old browser - Specific version of browser
May be a bug on the browser is sending an incomplete request, which by coincidence happens to be an invalid one and that points to a non-existent resource. May be the browser has a cache defect and is sending the 404 response without even checking the resource. You test this by using at least two different browsers and private session, that way you discard browser problems, caching and cookies. (This works only for JS).
Requests originated on a specific location
That location may have connection problems, or a defective ISP, or an overzealous caching service, or a problematic proxy. You can not test this, but you can try to detect it and react, for instance, not sending ads to those requests.
Firewall - proxy
Is your client's site name similar to a banned/blocked one? If so, and if by coincidence on a server has happened a typo, you may be affected each time a request passes though. Check on lists of banned sites.
Overload on your clients server
Is your client's site hosted on a shared hosting, or a hosting that may be overused? If so, strange behaviours may happen, for instance related to execution time limit of the command, or because it stablishes too many connections and some have to be dropped out, leaving some connection just hanging and waiting for answer. This is difficult to test, but you can check the server load, do a reverse IP check to see if there are many clients sharing the same IP, do cURL requests and check average time.
Time limit - redirections
There are different time limits on a whole connection process. You can check if there is a problem with this, at least from your system as user and from your client's server. Create a PHP file with a cURL session (fresh connection each time and reusing connection), execute it many times, and check the response time and redirections. Check if you always get the right response from the service, if it takes too long, if there are redirections, if there are redirections every time or just some times, test a different times.
EDIT (from Lajos Árpád)
Ad size mismatch
The code might be applicable for a given size, while you might use a different size. You should try to get information from your client about the issue.
Setting mismatch
This is a more general case for the above, but I described the problem of ad size independently, because ad size mismatch often occurs and it might be the real problem. Also, you should check whether the other important settings match, is there an issue with mishandling of something.
END OF EDIT
In my opinion, this should give you the answer you are looking for, and if it doesn't, you can provide more details on this question that can be useful for somebody else or use the results to ask/report on Google.