AlecJames, I'm assuming you made the object in a separate program and imported it into Anim8or, or used a script to do the boolean operations. If not, my apologies, but either way you need to pay more attention to the mesh structure. Also, as ENSONIQ5 stated, there was nothing really wrong with the face in question, aside from the problems mentioned below.
Your model has several problems. You had edges floating out by themselves for no reason, had another couple of edges connecting points where they shouldn't have, the tesselation needed improving on several faces since it caused concave polygons, you had duplicate points, and in general stuff just needed fixing.
I'm attaching a .an8 file that contains both the "fixed" version and the original. Be sure to compare the two objects to see the changes I made. It "should" export and slice fine now, but I may have missed something.