Glad to hear you seem to have resolved your issues. I am still concerned that something is not quite right with your setup because you are unable to use 127.0.0.1 (local loopback address) in the network settings of the server itself. Both 127.0.0.1 and 192.168.1.100 (server LAN ip) should work interchangeably in your particular scenario. The standard accepted practice is to use 127.0.0.1 (and only 127.0.0.1) in the network settings of the server itself.
The following test should indicate that 127.0.0.1 is working.
In server app - go to the DNS Service Settings and make the following changes: (temporarily for this test)
Edit the forwarding server list - and remove the forwarding servers (they are not actually needed - explanation follows at the end of this post).
Edit the permissions - set to Allow Connections from Private Networks only.
Set the perform lookups for Only Some Clients
Edit the lookup client list and select The Server Itself and Clients on the Local Network
Stop and start the DNS service.
For the purpose of this test lets assume that your hostname is server.example.com with LAN IP of 192.168.1.100 (you will replace server.example.com with your actual host name in the subsequent steps).
Open system preferences and go to network settings.
Select ethernet and click Advanced.
In the DNS tab - remove all DNS server IP's and any search domains.
Add 127.0.0.1 as the only DNS server - and in the search domain enter your domain name (in this example you would use example.com the domain portion of your host name)
Apply the settings.
Open a terminal window (on the server itself)
At the command prompt enter: host server.example.com (you will use your fully qualified host name) - it should respond with 192.168.1.100 as the IP.
Next enter: dig -x 192.168.1.100
it should show you your A record, PTR record, NS record
If all is working perform an external DNS lookup such as: host google.com it should report the external ip. Try some additional external lookups.
Go to a client computer - system preferences - advanced (wifi or ethernet) and set the DNS server to 192.168.1.100 and change the search domain to example.com (substitute your actual domain name).
Open a terminal window (on the client) and perform the same tests as on the server. The lookups should indicate success.
If everything is still okay set the client back to getting the DNS and search settings from DHCP. Renew the DHCP lease on client. Test with the host and dig commands from the client again. The lookups should be successful. If not - you have something not set correctly on the Airport router.
Back on the server I would suggest leaving the DNS settings at 127.0.0.1 and search domain of example.com. I would also suggest leaving the permissions set to Private Networks (you are only using this DNS server from within your private network). You can choose to put back the forwarding servers - or try running without them for a few days.
Note on forwarding servers: The DNS server in OS X is fully capable of performing all of your DNS lookups (internal and external) without the use of forwarding servers. It will cache all of the lookup results until the TTL values expire. Depending on your mix of DNS queries - the OS X DNS server may prove to be more efficient without the use of forwarders - but typically the forwarders will improve performance on external lookups. When you specify one or more forwarding DNS servers - the specified forwarding server(s) is/are used for "all" DNS lookups outside of the zone for which the OS X server is authoritative. OS X Server will look first in its own cache before querying the forwarders. Once a forwarder is specified - the OS X Server DNS server will no longer resolve external addresses it own (meaning that it will not query the root servers) - it will always use the forwarders. Typically a forwarder is going to respond quicker than the internal OS X DNS server - but if your typical DNS query pattern is limited to a handful of commonly accessed websites or host names - the OS X DNS server may prove to be more efficient.
If you can't get the 127.0.0.1 to work - you need to continue with troubleshooting - otherwise you may have a DNS issue that is lurking in the background - which will likely cause a lot of grief at a future time when it is harder to fix.
~Scott