The Insider.com article 'We could have lost the Apollo 11 crew:' A once-classified anomaly nearly killed NASA's first moon astronauts, a new book reveals describes a problem during reentry of several Apollo missions where the Service Module jettison did not execute properly and so it remained dangerously close to the Command Module.

There is a lot of technical information in the NASA links. There seems to have been some sort of problem with sloshing that prevented the Service Module from continuing to move away from the Command Module, and this was addressed by a Service Module modification implemented for Apollo 14.

Question: How did sloshing prevent the Apollo Service Module from moving safely away from the Command Module and how was this fixed? //

...the service module, upon being jettisoned on a lunar return flight, should have entered the earth's atmosphere, then skipped out into a highly elliptical earth orbit. Thus, the risk of recontact with the command module during entry would have been eliminated. However, on Apollo 8, 10 and 11, the service module did not skip out as expected. //

they reduced the roll burn time to get the proper roll rate and simply commanded the -X thrusters to burn for only 25 seconds instead of burning to propellant depletion. The service module would still tumble due to the sloshing, but without the thrusters firing, it wouldn't accelerate back toward the command module. The shorter separation burn would not be enough to prevent prompt reentry of the service module, but apparently that wasn't a necessary feature of the operation.

I think the article greatly overstates the seriousness of the anomaly, by the way; it didn't "nearly kill" the crew of Apollo 11.