I screwed up a couple of takes yesterday when I had knocked the shutter speed wheel onto a setting other than 1/50 without noticing.

I'm wondering, if I left shutter speed on auto to stop this happening again, would the Z1 ever change it from 1/50? I don't remember ever noticing this happening. It never goes slower and it just prompts for ND filters if there is too much light. I want it on 1/50 all the time unless perhaps I'm doing a static shot after dark.

The only way to keep it on 1/50 is to set it to 1/50 in manual. If you leave it on auto, it wont go below 1/50, but it will increase when it is adjusting exposure. Why don't you try using the manual lock feature?