When I was watching Worst Cooks in America, I was starting to get annoyed at the emphasis on knife cuts. I completely understand that things cut to the same size will will cook more evenly, but if I had a week to work with a new cook, I don't think we'd be spending a lot of time on matchstick cuts.
Teach the person how to use a knife so they don't lop off an appendage, and show them how to use a mandoline if you really need precise cuts. Then move along. Perfect cuts are nice, but for me it wouldn't be as much a priority as some other things. Like taste. If the person was a fast learner, we might revisit knife cuts again later.
I was also stumped as to why they didn't let anyone use a thermometer to figure out if meat was properly cooked. Yes, it's a good skill to know how to test meat by touch, but thermometers aren't an exotic gadget. Better to use a thermometer and know that the roast is done before you cut into it. So I'd teach people how to use a thermometer, how/where to insert it in different cuts of meat, and what temperature relates to what doneness.
I think I'd also do some teaching about shopping. How to you choose the freshest vegetables, and what to look for when you're picking up a package of supermarket meat or what to ask the butcher for.
And maybe at least one lesson on improvising. Making soups and stir-fry dishes without recipes. Maybe a lesson on re-purposing leftovers.
Possibly a lesson on how to look at recipes and figure out substitutions.
What would you teach newbies if you had a short amount of time and you wanted them to end up being a decent home cook when you were done?