the photos didn't show up so here are the links:
Mint:
http://www.flickr.com/photos/31518087@N05/3739928999/

Mystery Plant
http://www.flickr.com/photos/31518087@N05/3740723992/

The minty plant could be pennyroyal? Just a guess-- I'd do better if I could smell it.

Your mystery plpant is one of the nightshade family. Assume it's toxic in all parts.

The "mint" ... don't use it unless you can absolutely identify it. Pennyroyal has enough of a "minty" taste that people have made themselves very ill using it in iced tea and juleps.

Your "mint" does not appear to be a member of the genus Mentha (the true mints). The square stems put it in the family Lamiaceae which includes: savory, basil, mint, sage, and many other herbs. Pictures of the flowers and a close-up of the leaf would help greatly in identifying the plant.

It could be Clinopodium vulgare-common name Wild Basil. I'm not sure of the origin of the common name as it has very little in common with Basil (Ocimum sp.) and is not closely related. Clinopodium vulgare is a widely distributed weed closely related to calamint (Calamintha sp), which is another possible i.d. for your plant. It was at one time classified as a species of Satureja (the genus that includes savory and yerba buena). If it is Clinopodium vulgare, it should begin flowering very soon.

F. DeBaggio

Here is a link that might be useful: Photo of Clinopodium vulgare

Your mystery plant is a Solanum, a plant in the nightshade family as lazygardens mentioned. It looks like Horsenettle Solanum carolinense to me.

FataMorgana

Mystery plant is horse nettle for sure. Grasp the plant at the base while wearing heavy gloves and pull it, and as much of the roots that you can find, out of the ground. It will continue to sprout from roots.