You got more guts than I; I wouldn't even touch that FPE panelboard. I'd be too worried that if I took off the cover, all the breakers would come out with it....
Is that AC/MC feeding those spot lights in the first picture...?
As an aside, the tenant may not be an electrician, and it may not even be their responsibility to make any repairs at all, but it sure wouldn't be hard to buy and mount some 50ยข cover-plates to help safe-guard her kid.