Assuming you are feeling good at your current dose, I think you will know if it has "gone bad" because in two more weeks or so you will start to feel hypo again. But unless you were opening the bottle when the room was still very hot and humid, you are probably okay. In the future you might want to try storing it elsewhere, like beside your bed or in the kitchen-- wherever you would see it first thing in the morning.
"Proper storage of Synthroid:
Store Synthroid between 68 and 77 degrees F (20 and 25 degrees C). Brief storage at temperatures between 59 and 86 degrees F (15 and 30 degrees C) is permitted. Protect from heat, light, and moisture. Do not store in the bathroom. Keep Synthroid out of the reach of children and away from pets."
- Drug Information Online - Synthroid.
I've always stored my thyroid med in the bathroom medicine cabinet and have never had any problems. Make sure the bottle is closed tightly all the time. If you feel more comfortable, store it in another location, out the reach of children.