ZS4 imports and outputs .avi video files.

To convert your .mov files to .avi files for import into ZS4, your best bet is probably mencoder.
You may already have this installed on your Linux machine but if not, you can get Linux and Windows versions from the MPlayer website.  Make sure the libavcodec gets installed as well, in case you don't already have it.

Try this command to get a format that ZS4 can read:

mencoder -of avi -oac pcm -srate 48000 -af resample=48000:0:2 -ovc lavc -lavcopts vcodec=mjpeg inputfile.mov -o outputfile.avi

I specify with -srate and -af that it should convert the audio sample rate to 48khz (well), in case you have files that have a lower rate.  ZS4 outputs only 48000khz audio and does a fairly rough conversion.