There is no widespread mail problem on cPanel 11.38 that we are aware of, so this would not qualify as a "known" issue. There were some improvements in settings and small changes in the Exim Configuration Manager, but no major changes in Exim itself, in the update from 11.36 to 11.38.
Please explain the problem you have encountered in greater detail. If this is affecting your service, please submit a ticket using the link provided in my signature so we can investigate it and help you directly.
The major problem with our clients was they were unable to send emails from the server. Neither bounce back nor any logs in the exim_mainlog.. So we usually used to move the /usr/loca/cpane/etc/exim directory and ran upcp on the server. It fixed the issue..
As this issue occurred while upgrading the cpanel to 11.38..
We have not seen widespread reports similar to yours, which is why I said it is not a "known" problem.
You may well see the same problem on several of your servers, but that does not mean it is happening on every cPanel server that has been updated. You need to consider what customizations you may have made on all of your affected servers. Yes, you may notice a pattern on your servers, but they may have something in common that is not the same with all cPanel installations that just got an update.
Anytime anything provided by cPanel stops working, especially after an update, please do not hesitate to submit a ticket so that we can investigate the problem, fix it, and if it really is something that is going to cause a widespread problem, we can alert our developers.