I tried a variety of things, including a variety of corner guards and edging to cover up the finger joints. Results were usually more trouble than they were worth.
In the end I settled on a very simple method: an additional "faceplate". A second panel that covered the presentation side of the enclosure and also provided any labels or marking.
So instead of the top of a unit looking like this (note the visible finger joints around the edge):
It now looks like this:
|(Image: Timer / Scoring Unit built for a local air gun range.)|
Separating the "presentation" panel from the enclosure itself has other advantages. You can use a different material since it's not part of the structural design. Here's an example of a layered-wood prototype that uses a black-and-white plastic top panel covered with a clear plastic shield. Using layers of wood for the enclosure itself and a high-quality engraved plastic top gives a really nice result.
|(Image: a prototype for a product that went nowhere)|
Using a separate, additional panel as a faceplate turned out to be a useful method. I can keep the utility of finger-jointed or layered boxes but give a much higher quality (and durability, if needed) to the "presentation side".