As others have suggested, paying referees may improve the quality of their reviews. However, I believe that payment should be restricted to those referees who provide reviews within a defined period; say, two to three weeks or less.
Each journal could develop a process whereby authors who want a manuscript reviewed expeditiously would pay a nonrefundable fee at the time of submission. The fee would be based on length; a fair price might be $5 per typed page. To set the fee, each journal could conduct a survey to determine the average actual length of time a referee takes to read a manuscript N pages long. I usually limit myself to five hours per manuscript. On the basis of reviews I've received, I would guess that many referees spend less than two hours per manuscript. The fee charged to authors would be paid to the reviewers if they return their reviews within the specified time.
This process would provide an outlet for those aggressive authors who want more rapid publication of their work without penalizing other, less anxious authors with higher page charges. The extra fee would also prevent a flooding of manuscripts into the acceleration process, which seems to have dramatically delayed the average time for papers submitted to rapid communication journals that were originally established to avoid such delays.
Other indirect benefits include a reduction in the length of papers submitted and perhaps a reduction in the number of papers as well. Several journals with rapid communication sections limit the length of the manuscript so much that very little space is given to details of methodology. My plan would not limit manuscript length, thus allowing improved quality of data.