These logs are helpful. So a couple of points to note here which are causing the issue:
1. You log file shows that you have 2 network paths defined in your configuration file:
2014-02-18T19:31:57 MCEBuddy.Engine.QueueManager --> Attempting to connect to network share \\192.168.1.24\freenas\Media\TV Shows\At Midnight 2014-02-18T19:31:57 MCEBuddy.Engine.QueueManager --> Attempting to connect to network share \\192.168.1.24\freenas\Media\TV Shows\
Both network paths are pointing to the same server and it is being authenticated twice (once in your monitor task and once in your conversion task). You should NOT authenticate the same network location twice, once is enought, so your monitor task is redundant.
2. Your network share path \\192.168.1.24\freenas\Media\TV Shows\ is incorrect. Network share paths don't end in slash '\'. That's why the second authentication is failing. I will put a check for this in the next build3. You are using PostCustomCommandUISession = True in your Custom command parameters. Why? I hope you're read the documentation carefully. This causes MCEBuddy to use the active logged in users's session to run the command. That has SERIOUS implications, like network driver mapped by MCEBuddy in SERVICE Session are no longer available in USER session. This is ONLY to be used if you are running a program that needs access to DirectX/hardware API's.
Point 3 is likely why your custom command unable to access the network share.