Carol singers huddle around a sparkling Christmas tree in a snow-dusted village as warm light illuminates the stained-glass windows of the church on the hill and a crescent moon hangs in the starry night sky.

As a classic Christmas scene the picture is hard to fault, but in the eyes of one astronomer there is a lesson here about the workings of the heavens that many of us could learn.

Peter Barthel, who studies quasars and active galactic nuclei at the Kapteyn Astronomical Institute at the University of Groningen in the Netherlands, belongs to that group of scientists who notice things that most of us, through ignorance or lack of pedantry, are happy to overlook. Things like Christmas cards depicting penguins cavorting with polar bears, or designer snowflakes that "corrupt nature".

For Barthel, the last straw was a Unicef Christmas card in 2010 that showed three bobble-hatted children decorating a tree on a snowy hill beneath a waning crescent moon. The scene is unlikely, says Barthel. A waning moon, which looks like a "C" in the northern hemisphere, doesn't rise until around 3am, and reaches the height in the card an hour or two later.

"I don't think the children would be out at that time," Barthel says.

The scene at the top of this article, from a digital advent calendar in 2010, makes the same mistake. The picture, with shops aglow and child choristers joined by their pet dogs, is firmly of the evening. But a moon that thin and waning is only visible in the early morning in the northern hemisphere.

"One cannot exclude the possibility that both artists had the inention to create Australia scenes with reversed moon phases, but the presence of snow in both scenes is strongly suggestive of the northern hemisphere in December," Barthel says.

The astronomer has put his pedantry to good use in a paper accepted for the journal Communicating Astronomy with the Public. In it, he surveys images of the moon on Christmas cards, wrapping paper and children's books in the Netherlands and the US. The moon was wrong in 40% of Dutch books and 65% of Dutch gift wrap. The US fared better because most cards, books and wrapping paper showed the full moon instead of the trickier waxing and waning ones.

"The lack of knowledge concerning the physical origin of the moon phases, or lack of interest in understanding, is found to be widespread," Barthel concludes. He discovered similar mix-ups in Halloween images.

In the paper, Barthel answers the question that fast comes to mind: who cares? The errors are innocent, he says, akin to impossible rainbows that have the red arch drawn on the inside instead of the outside. "Now, watching beautiful natural phenomena like rainbows and moon crescents is one thing, but understanding them makes them all the more interesting. Moreover, understanding leads to knowledge that lasts," he writes.

The phases of the moon are easy to grasp. A full moon is directly opposite the sun with respect to the Earth, and so rises at sunset and sets at sunrise. A waning moon, moving from its third quarter to a new moon, has its left side illuminated to create this shape ( in the northern hemisphere. It rises around 3am and is visible very late at night or in the early hours of morning.

A waxing moon, on the way to its first quarter, has its right side lit and looks like this ) in the northern hemisphere. This type of moon is visible from afternoon twilight into the evening.

Click here for an animation of the moon's phases.

Barthel is less troubled by images of Santa Claus delivering presents to the world's children in a single night from a sleigh pulled by flying reindeer. "That's a miracle we do not understand; the moon phase we do understand, so why not draw it correct?"