I have an abscessed #19 molar (x-ray attached). Would you refer this for endodontial retreatment or extraction? (photo)

This is an easy one.  The odds are that you have a small crack somewhere around the roots of the tooth.  In my opinion, a retreat would likely not be successful.  I would recommend to have an extraction, bone grafting, and an implant placed.  This will cost more, but you will not have to worry about it in the end.  Good luck.  

I would also recommend an extraction. As the abscess permeates the entire tooth, it is likely fractured. A fractured tooth cannot be fixed and is best to be extracted.The choices for a missing space would be implant, bridge or partial. The implant is the best, and it would be beneficial to take antibiotics before the tooth extraction and while healing with a bone graft in place to aid in implant success. While an implant takes longer to do, and is more costly upfront it rarely needs to be redone.

It is not looking good for this tooth.  Current root canal looks pretty good (not perfect but then little in the world is) I suspect that there is a split root here.  Get the consultation with the endodontist in case there is something obviously wrong in his eyes with the existing treatment.  If not, an implant replacement would probably be  better way to go.

Sometimes the shadows on xrays mean a root is fractured, so retreatment will not work.  Ever.  Retreats under normal circumstances can be successful, but often the cost of an alternative (implant or bridge) is the same or less, with more predictability.In this case, I suspect an extraction would be better.