I read somewhere that the most common errors in backgammon play, even among the strongest players, derive not from choosing the wrong move from an available selection, but from failing to spot a move altogether. Is this true? And does anybody have any particular tricks or habits to minimize the occurrence of such oversights?

Overlooking plays isn't the most common source of errors, but they do tend to be the biggest errors. Missing a winning outfield hit, for instance could be a quadruple or quintuple-whopper. However, the sheer number of plays where you see the right play but do something else anyway overwhelms the occasional oversight.

The two good ways not to miss a play are (1) use the time spent shaking the dice to look around the board and notice what numbers you need to hit blots, and (2) get alert when you roll a double and spend extra time making sure you see all the choices. A beginner gets excited when he rolls a double because of all the good things he can do; an experienced player knows that rolling a double gives him many ways to blunder, so he knows it's time to buckle down and go to work.

Here's a great strategy to overcome that problem:

Set eXtreme Gammon to play against itself and just watch the moves. Once in a while, you will jump from your chair, because it will play a move you have not seen.... the kind of move you typically overlook in your games. Slowly, your brain will assimilate the new possibilities. Great way to 'see more'.