How to disable MDNS

mDNS doesn't affect regular DNS, so that's not the problem.

OS X does send DNS requests and replies like any other OS. For that matter, most modern OS's also have mDNS services. Bonjour (Apple's implementation) is available for OS X and Windows, and there's Avahi for Linux and NetBSD systems. Windows CE has a similar function.

When a machine in a network needs to resolve a host name, it sends a DNS request to the list of DNS servers manually configured or provided by DHCP from the local network's DHCP service. If a machine wants to perform local service discovery on the LAN, it instead sends out a multicast DNS request and a system on the LAN replies. Fundamentally, the requests are handled differently and don't interfere with one another. mDNS doesn't respond to regular DNS requests (which your switch or router shouldn't even make visible to the other systems on the LAN), and systems with mDNS do not use it to replace standard DNS requests.

On Windows systems, you can disable mDNS by disabling the Bonjour (if present) and ZeroConf services in the services administration panel. In Linux, you disable it by logging in as root and typing

$ service avahi-daemon stop
$ service avahi-dnsconfd stop

In OS X, you can disable it by opening terminal and typing the following:

launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponderHelper.plist

... this is unlikely to resolve your problem as mDNS is not likely the cause. Disabling mDNS will disable service discovery on your local network, so file shares, printer shares, photo and music sharing, screen sharing, etc. can all be affected.