It looks like you have male adapters at the valve body and a nipple and cap where the spout will go. This is typical for this type of faucet. If the leak is where the male adapters enter the valve body, it is likely you didn't tighten the threaded connection enough. Pipe threads are tapered; the more you tighten, the better the seal. With steel, it is almost impossible to damage the fitting; with copper and brass, you have to use a little less than all your strength, but put quite a bit of torque into it. Use an open end wrench to avoid rounding off the flats on the male adapter. I would go 4 or five times around with the Teflon tape.
Your post at 2:28 pm (local) yesterday is the right procedure, especially the wet rag. If you still have a leak. you can cut the straight pipe leading into the valve body, tighten the threaded fittings, and sweat in a repair coupling, repeating the wet rag trick. It is possible you got the male adapters cross-threaded, but it doesn't look like it to me. If all else fails, check for that.
If one of your sweat joints is leaking, you'll need to get the joint completely dry, heat it to melt the old solder, flux it and re-solder the joint. The supply tube at the bottom will not drain unless you cut it at the low point. Mapp gas gives you more heat than propane and will help dry things out quicker.
You did a good job. These things happen. Good luck.
"Never try to teach a pig to sing. It wastes your time and annoys the pig." Robert Heinlein
"[H]e had at home a lathe, and amused himself by turning napkin rings, with which he filled up his house, with the jealousy of an artist and the egotism of a bourgeois." Gustave Flaubert, Madame Bovary