I use a sharp paring knife to cut rind off of fruit. I find that I have better control of how deep I go with a knife than when I use a peeler. If I have white pith on the under-side of the peelings, I just hold them down flat with one hand, and then holding the paring knife horizontally, I am able to cut off the pith. As far as the dated broth... many dates are just a company covering their own... Some expiration dates are just a way of saying that it would be better to use something by such a date. With something like broth outdated by a month, if it smells O.K., I would just use it. I have put something in a pot and boiled it for a while thinking that I would be killing off anything questionable. That is probably not an exact science, but I haven't killed anyone off yet.

Broth in a shelf-stable box has expiration dates that can be taken with a grain of salt. As always, be observant: if it is puffed and bloated (which would likely be the result of a breach of the packaging) don't go any farther, just get rid of it. If it looks right, smells right, tastes right, I would feel comfortable about it. If not, "then pitch it and get to the store!"

I like a veggie peeler to do strips of lemon, amysarah is right about the pith, it's quite bitter. I also think the broth will be fine, especially if it's canned. I'd open it ahead of time to make sure. If it seems funky, then pitch it and get to the store!

On the expired broth, probably the worst you can expect is a slightly off color and/or texture, perhaps watery looking. Safetywise, I'm sure you're fine. If you can, have back-up cans of broth available in case you ust don't like the look of it.

Lemon peel strips: I use a small sharp paring knife; just be careful not to cut too deep - the white pith under the skin tends to be bitter.

Chicken broth: personally, if it just expired last month, I wouldn't hesitate to use it. (For something like canned broth, I think there's some reasonable leeway in the exp. date - but if you're concerned, maybe someone else here will have the official word on this.)