I actually think that a better vetting process is a good idea, and that it should be applied to all and sundry both for fairness and because much of the potential threat but by no means all of a potential threat is lodged in these nations. As this was such a centerpiece of his campaign for so long, however, I am a bit frustrated that a more complete process is going to take 4 months to get in place. Should have had people working on the specifics from 11/15 on
What in particular could be improved in the process, arduous as it is? Is anything concrete meant to be achieved by such a reform, or by an intention of reform?

This isn't a question of process after all, but one of source. Some classes are prima facie unacceptable, others are not, and all before any paperwork or interviews come into play. The contest now is whether "Muslims" may be considered among the unacceptable classes.