Q: "There is a problem with a family member's previous purchase"

I just had the same problem but after a bit of digging around discovered it was straightforward to fix.  My card had been cancelled after being cloned and after I updated my account started receiving the same message. 

It turned out that there was an outstanding balance on my daughter's account (via family sharing) and the fix is to log in to iTunes as that person and go the previous purchases in their account.  You will be presented with a message that tells you how much is outstanding, and given the ability to pay it (using the three digit code on the card signature strip for authorisation).  Once the balance has been cleared everyone's account springs back to life!

In my case, I was unable to pay for the previous purchases for my wife's account since the credit card on file had already been closed.  Apple asks for the three digit code on the existing (closed) credit card but provides no way of replacing the credit card entirely -- at least, without temporarily disabling Family Sharing.

same joke here. credit card valid until 2017, cannot update anything...

Same. I followed the suggestion of logging in to my son's account and did see that there is an outstanding charge of .99 that came through after my credit card expired. I'm now stuck in a loop... I am unable to update my credit card (I'm the family organizer), I am unable to remove my son and add him back in as he's under 13, and when I'm logged in as him and it asks for the credit card security code, it won't accept the expired card's number. Stuck stuck stuck. Please help!

@jcybillI I had the same issue (of course).  I was able to log into each of my family members iTunes account > click on  "see all" under purchase history.  I found one failed purchase.  I was them able to re-type the CCV from my current credit card.  After that all the updates and pending purchases worked like a charm.

Unfortunately that wouldn't work for me. I spent 70 minutes on the phone with Apple today and they sorted it for me!

I had this problem.

There may be other solutions to this but what worked for me was to disable Family Sharing, update my payment info, then re-enable Family Sharing.

I couldn't personally find any other way to save my new card info and make the change actually "stick" without doing this.

TThanks this worked had to remove my wife from the family. I guess apple doesn't like happy homes.

That was the problem.  It must have to do with an outstanding balance on any of the id's on the family sharing. 

Thanks.

Everything @Rob__T said was correct, with the exception that it is also possible that the billing error may be tied to a family member's iTunes account and not the actual organizer's iTunes account. You will have to login to each of your Family Member's iTunes accounts that are linked to your Family Sharing to find which has the actual billing alert where your payment information is listed requesting that the billing information be updated.

I have this same issue - the iPhone will not update apps, but I can't identify what the billing issue is.  Apple iTunes billing support pages indicate that you should be able to see the billing issue, but I can't.  From either the iTunes app or from the web, when logged in as the family member with the problem, it does not show any billing issues. The help page claims "If there's a problem with a previous purchase, you'll see a message when you sign in to the iTunes Store or try to make a purchase." but this was not my experience.

We corrected the payment card issues with the family organizer, but this one family member is still broken.