3-Way Light Switch, two blacks and a red?
It sounds like your wiring is like this:



I believe the switch you took a picture of is the one on the left. If so, it looks like it's wired correctly: the black screw is usually common, and it seems to be coming from the red wire nut, which is the power source (am I seeing that correctly?) 



If the other switch is turning on/off the light, regardless of which position this switch is in, then it is very likely this is a defective switch.

However, if it is only happening when this switch is in one particular position, then it's highly likely one of the two switches has the common wire connected to one of the traveller terminals. It could be either one. 

If you can determine which wire goes where (the biggest hint is that the traveller wire is 14-3 while the others usually aren't), then you should be able to match it up to the wiring diagram here.