As a long time apartment dweller, I say aye to the OP’s list and add a small cordless screwdriver operated on AA batteries for the thing drawer (for those times when you don’t want to drag out the big cordless drill, which will be more often than not in a small apartment). They run ~$12.
Heavy duty scissors, a bag of wire ties and an eyeglasses repair kit (even if she doesn’t wear glasses, those teeny tiny screwdrivers rock for things like iPods and cell phones) would make good additions as well.
While you’re using those flashlights to look for things under/behind furniture, a yardstick is handy for actually getting stuff out. (You can even use it for measuring, too!)
I also like to have a pack of disposable plastic gloves and some cheap plastic scrubbies.
Thirding or fourthing the “no cordless drill” sentiment. As a long-time apartment dweller, I used a drill maybe four times a year, so it was never worth dealing with the additional space and forethought that the charging setup requires. A compact corded drill with a 20 foot extension cord wrapped around the handle can live in the back of a closet, and handle basically anything an apartment dweller could ever need a drill for.
An AA-powered electric screwdriver isn’t a bad idea, though.
My first thought was, “Why in the world would anyone need that?” Then I read the description and was duly impressed. It would help loads when lining up pictures.
The first things that came to mind were basic tools (hammer, nails, screwdrivers, screws, wrench), tape measure, tape, flashlight, scissors, and batteries of varying sizes. Looks like everything I thought of has been covered so far except batteries, so get those.
A package of assorted sizes of zip ties (one can never have too many zip ties!)
Picture hooks of various sizes
A measuring tape (I couldn’t live without mine)
A kitchen fire extinguisher
Some cable clips to secure wires along the baseboards
