What you're hearing could be the result of a sampling-rate conversion issues, although I can't be sure without having heard an example recording.
You're using an external audio-interface, which has it's own A/D-conversion hardware, running at a certain configured sampling-rate (44100Hz, 48000Hz, 96000Hz etc…) . When your mac's internal audio-hardware uses a different sampling-rate, my experience is that this can result in the clicking noises you describe.
(I would rather describe it as a 'rattling' sound)
To prevent it, make sure all audio hardware uses the same sampling-rate. It's probably also best to make sure any file-inserts (audio-, video-files etc..) that mix in additional audio-tracks in ScreenCast, also have that same sampling-rate.
And personally I would even go so far as to avoid sampling-rate down-conversion at the encoding stage. So if you've for instance configured all your audio-hardware to sample at e.g. 48kHz, then also encode your stream audio with this sample-rate.