My first guess is seed are from an inadvertently cross pollinated plant. Second guess is blossoms are being pollinated with pollen other than from same plants. It could be from a nearby garden or cucurbits growing in the wild. If taste is satisfactory I wouldn't worry.

It should be understood that either before or after harvest, squash may get what is called "chilling injury" that makes for sunken pits on the surface and high levels of decay in storage. This happens when temperatures drop below 50F. Did these squash start to appear this way after it cooled off?

klem, I'm thinking I may buy a new pack of seeds for next year in case that's the problem.

dan, these have come out this way all through the season. We were hot during the day and most nights it stayed in the 70s and 80s until recently we've dipped with Autumn approaching.

carol, I haven't seen any insects that aren't the usual in the garden, and the leaves looked fine all season with no insect damage apparent there. Virus? Would that be in the seeds or my soil?

Not a botanist, so I can't tell, but have you contacted the company yet and shown them the photo? I would.

You might consider squash (or cuke) mosaic virus. This image of a mottled squash looks a whole lot like yours.

https://plantpath.ifas.ufl.edu/u-scout/cucurbit/squash-mosaic.html

Of course, you'd expect blistered leaves as well, but allegedly the symptoms start on the fruit.

carol, I've only asked here and haven't contacted the seller about it.

dan, followed the link and squash mosaic does look like it could be the culprit. If that's the case, then it's due to beetles and not something in my soil. I'll have to check out the leaves to see if there's any blistering. I read where it said commercial growers can't market squash that get this virus. I know as a home grower, I couldn't give any away this year!

It's the first time this has happened in all the years I've had zucchini or squash, so hopefully, next year will be back to normal.

You might look for mottled leaves, raised dark green blisters on fruits, and stems that dry out rapidly. That would clearly point to squash mosaic. To the extent the seeds came from a reliable source, it's unlikely the virus came through the seeds. But soaking the seeds in 10% bleach will kill whatever is on them.