When is it beneficial to use the double precision solver for fluent? I can't seem to find a real answer to this anywhere.

Thanks.

The use of double precision in Fluent is basically the same than for any other numerical code. It is needed everytime you need to capture a small variation of a quantity that can vary by large amounts. For instance if you have a very stretched mesh, with some cells dimensions beeing way higher than others, double precision will be helpful.

If I have models which are giving me many incompletes on the DPM, would double precision help eliminate them?

Most likely not, incomplete in DPM means that you are not having enough integration steps on your particles, or that the step are too small.