Well as Vrakthris advised, the best option will be to submit a ticket and make a post which should probably go on the Mac Technical Support Forum (link below). There doesn’t appear to be a known issue impacting players that Blizzard is tracking, and the error code does indicate a that its related to your computers network connection. I know I personally was able to resolve the issue simply by rebooting my computer which completely reset my network connection, simply shutting down battlenet did nothing, so definitely try that.
Here is a link to the forum