So you invented the tablet computer but not cloud computing? Or even network file shares...
Instead of "Hey Captain, I need you to read this document and sign off on it, please see the attachment" you could just hand him a physical device with the document on it, he'd read it, press the "make it so" button on the bottom, and hand it back or have it sent back to the originator. He couldn't neglect it or forget to look at it, because there'd be a physical token associated with the file, which could itself be tracked through the ship at all times.
I wonder if this will be a trend, in fact. Getting away from "one device that does everything" and more towards "a large number of identical devices for different functions". Give me a pad that handles my email, a pad that handles my calendar, a pad that handles my to do list, and hang another one on the wall for use as a videophone. Then maybe I'll have a pad which reminds me where all my other pads are.
NB. I've watched, like, three episodes of Star Trek in my life.
The overhead of opening files from a file share or e-mail is not a major impediment to my productivity.
A more fully thought-out future might have a desk that was a hologram where virtual reports are still "stacked", with these serving primarily as a metaphor for both Picard and those watching Picard (they could judge how busy he was by how many "reports" he had stacked on his holographic desk).
After watching a couple of scenes with Picard having several PADDs on his desk it occurred to me that I was presupposing that those devices were personal property. But in that future personal property is largely for sentimental items, not utilitarian ones. Also, the PADDs are primarily computer iterfaces.
If you posit that PADDs are as ubiquitous and disposable in the future as Post-It notes and thumb drives are today, the metaphor makes sense. (Indeed, considering the inevitable price drop of consumer electronics, we aren't that far away from iPadish tablet computers reaching that point.)
So Riker picks up a "blank" PADD, his DNA and thumbprint or whatever identifies the device to the network as a Riker interface for the time being. After he's composed his mix tape or status report on the device, it's also resident on the network. And when he hands that PADD to Picard, the recognition of the transfer to Picard serves to automatically track the work flow and acknowledge Picard's acceptance of the report.