Is this swing beam safe?
The usual disclaimers apply. I'm not a licensed structural engineer, I'm not providing engineering advice, I'm just reporting what standard load calculations in the literature say, etc....

Assuming no major defects, and using #2 graded southern yellow pine in wet service (the least optomistic numbers), with an actual size of 3.5" x 5.5" (typical of planed "4x6") a 415 lb load at the middle of (aka point loading) the 12 foot span should be safe. 

Some deflection is normal. The above load should have a bit less than 1/2" deflection.

http://www.forestryforum.com/members/donp/beamclc_ctrpointload.htm

Uniformly loaded (not really applicable, but "the other extreme" as you interpolate 3 swing positions) 825 lbs, with a deflection a bit more than 1/2" (considered OK for a roof, too much for a floor.)

http://www.forestryforum.com/members/donp/beamclcNDS2.htm

There are some slight complications (about a 20% reduction in loading, IIRC)  induced by the cantilever overhang, but none should really be of great concern for normal-szed children. On the third hand, if you wanted to bolt/screw/glue/nail a pair of 2x10 or 2x12, one to either side of the swing beam, that should stiffen it up quite a bit.