I would try this first:
Start your day with a number of blank sheets of paper, 8 1/2 x 11 is fine. Put your common context headings at the top of each one. As you are asked to do things, jot them down on the appropriate sheet of paper. As you complete items, cross them off. At the end of the day enter any that are not completed onto your Palm. After doing this for a few days, evaluate what is working and what is not.
I find that when I am trying to figure out how to make a system work, it is best to go back to paper and then figure out how you want the process to work before trying to transfer it to your Palm.
There is no need to be completely digital or completely paper based. There is no reason why you can't have your calendar, notes, and personal tasks on the Palm and have your work tasks on paper. Whatever works for you.
PS. are you writing them directly into your Palm, or entering them on your PC and syncing? When I am at work I enter at the PC, which is much faster.