I assume you are talking about a SDVE or SW series pistol, is that right? If you are, technically speaking it doesn't have a firing pin, it has a striker.
Since you bought it used, it's probably not covered...S&W warrants the gun to the original owner only. They don't always ask, but it's better to be upfront about it, than send it in and then have them say they won't cover it.
Before you call S&W, though, a couple of questions:
1) Have you taken the striker out of the gun, and cleaned out the channel completely, and then dried it completely? Don't oil or lube the striker channel. (I know you said you had cleaned it, but I didn't know if you meant you just sprayed some cleaner in the channel, without removing the striker.)
2) Has the firing control group been modified? If so, the aftermarket springs may be the culprit. (If it has been modified, and you send it to S&W, they probably won't cover it anyway...since mods will cancel the warranty.)
3) When you say "light strikes", are you getting different primer indents? What kind of ammo are you using? Are the light strikes happening with different ammo, or just one kind?