Your plants are epiphyllums, commonly known as orchid cacti. Your
condition
is rather common. While it could be caused by sucking insects, the spots
are
more commonly caused by either water left on the plants in full sun
causing
sunburn (water drops act as lenses magnifying the light to burn small
round
patches), or by overwatering at a time of the year when the temps are
lower
and the plant cannot use or get rid of excess water. Epiphyllums are
rarely
hit by fungi, at least on the "leaves" (stems). And the most common insect
problem is mealybug which is easily seen. Give your plants a winter rest
by
reducing water and fertilizer especially if they're not in full sun or
receiving full natural light, depending on your location. Good growing.
Gary

Thanks for all that good information. The overwatering and/or too much
fertilizer is a condition that is quite possible. We used a LOT of water to
keep the pot heavy enough to keep from falling off the shelf. Dumb, dumb,
dumb gardening, I know...... perhaps lazy is also a factor.
Thanks again!
Lynn