The plant(s) will drop the mini-zukes that didn't get pollinated, which looks like that's the case with the ones in your first pic. If so it's fairly easy to correct. Either plant more flowers to attract pollinators or do the pollinating yourself. Of course you'll need both male and females blossoms to bloom at the same time to get fruit set and that might not have happened with those first ones (as in the females bloomed with no males open at the time).

Looks like you've got some zukes on the plant that will need harvesting soon unless you want them to become huge and seedy.

Rodney

They do like like unpollinated fruit. The problem should correct itself. a few of the leaves look droopy. Maybe you need to water a little more. How big is the container?

zucchini

Zuke, like any squash plant, will get very large esp. when happy. This advise may be a bit late - squash/zukes rotting are affected by irregular watering AND pollination problems.

Hand pollinate in early morning because the blossoms are only open til maybe noon.

IF blossom end rot - it is caused by lack of calcium to the fruit. Calcium is moved thru the plant by water thus irregular watering will cause blossom end rot.

I have not grown zukes (or tomatoes) in a pot for this reason but I do know the pots I do have dry out easily because of the wind and need daily watering. That means NO vacations, period.

For SFG, I give squash FULL sun in a 4ft square. You can get away planting two plants about 6in. apart in the center of a 4ft bed; tho it will fill the bed growing towards the sun so offset planting slightly to the north side is best.