No, NOT plumber's putty, pipe dope, they are different things used for different purposes.
And personally, I'd stick to the teflon tape. BTW, there seem to be two thicknesses of teflon tape in use. The thinner stuff does take about 7 laps to do a good job, but the thicker stuff only takes 3, or maybe 4 at most. The trick is always to get it screwed in tightly enough to seal properly.
See, pipe threads are supposed to be screwed in until the threads bind. The male and female threads are at a very slightly different pitch, so that when fully and properly engaged, they bind up on you, thus ensuring metal-to-metal (or nylon-to-nylon, as the case may be) pressure. The sealant is just to fill the gap in the middle to make sure nothing squeaks by.
If the fitting seems loose to you, there is no question that it is. And yes, it could be that it was screwed in too tight, and broke because of it. In which case you'll have to replace pieces, cause no amount of teflon tape or pipe goo or for that matter "silicone caulk" will ever give a broken fitting a good seal.