This request from the producer just seems odd to me - is there a reason for this concern? Did something untoward happen with an unsatisfactory outcome? Because - well, as mentioned, the list of potential issues is infinite and (Murphy's Law being what it is) won't cover what actually goes wrong, when it does.
That said, 1) in audio section, it's good you have back-up mic packs, but you never mention back-up batteries and where they live and; 2) in lighting, you are saying the SM does the dimmer check and mention missed light cues, both of which need to be addressed.
I could write a tome on preventative steps, but will just touch on a few things that come to mind immediately:
There shd be pre house-open light and sound/mic checks nightly, handled by board ops and repaired by whomever is appropriately responsible. If you are hired additionally to run boards (which happens more often in non-pro or smaller theater situations), a presumption that you will act as TD and replace lamps or solve sound cable/monitor problems is not standard. And missing cues more than once in a blue moon is, well, not ok.
You mention "stage going dark" - that implies a power outage. Are they so common there? And if they are, you need to include a way to connect w house so both cast and audience are safe.
And some of your list is basic job description.
Props: Preventative
Assistant Stage Manager will check that all props are in show condition prior to performance.
Assistant Stage Manager will ensure props are placed in proper positions for performance.
That is the ASM's job (whether they do it themselves or, in a union house, crew does it) and should not need to be spelled out as a preventative measure. That's like saying the SM will take blocking notes and call cues. If this is a problem, a serious conversation is in order.
You also mention things like your show having liquids on stage but not that you made sure there were rags/towels near or on the set (if appropriate) for wiping up spills - which will happen; nightly lock checks for the wheels of rolling set pieces; etc. So perhaps a more global perspective is needed to make sure actor/crew safety has been anticipated.
I have had boards crash midshow, mics fail, costumes rip, actors get injured, blown (or mistakenly thrown) fuses and many other bizarre and impossible-to anticipate mishaps. The bottom line is, are you able to maintain your composure - both within yourself and to keep cast and crew calm - and handle whatever comes up with grace and creativity, keeping the show moving forward where possible and stopping when safety is involved. Can you anticipate what might happen, proactively solve it in your mind, and then know that whatever happens, you have already dealt with it so you can handle whatever might arise.
There is an earthquake info document in the AEA SM packet. You might look through that and borrow that kind of detail and specific as a guide for making sure you have anticipated all aspects of your theater's potential issues.
And - good luck.