5 February 2013 Last updated at 04:53 ET By Louise Minchin BBC presenter

A mother's picture of her partner in his underpants was among the items carelessly made public over social media in a BBC investigation of parents and teenagers online for Safer Internet Day.

I consider myself quite canny about using social media without invading my own privacy. But there have been occasions when friends have posted photos of evenings out that I'd really rather had been kept private.

And I've seen them share more information about themselves and their children than is probably wise, when you think that information can be seen by millions of people worldwide.

But I've got a fair bit to learn - for myself, and as a mum. My eldest daughter Mia is just 11, and she has her own phone which she uses for messaging her friends, but she is not on Facebook or other social media. Yet once she hits the teenage years that's bound to change.

I came of age as the digital era was in its infancy, and I'm so glad that the internet, email and all sorts of social media have been available to me as an adult. They've enhanced and enriched my life immeasurably.

And I'm glad my daughter will have all those online tools available to her too. I just want her to be safe, selective, and think about how she uses them. There's a lot for all of us and particularly for young people to deal with in the online world.

My friend's daughter was only 11 when her school 'friends' posted really nasty personal comments about her on a public site. They were hauled into the head teacher's office, and it ended in tears with long-standing friendships broken for ever because they typed before they'd thought through the consequences.

And I know from friends with teenage children that the stakes get higher as they get older. Their kids accept "friends" they don't know on Facebook who turn out to be less than desirable. Vulnerable classmates have been drawn into 'sexting' - sharing intimate messages and pictures. Rows between rival groups at school get out of hand and insults are traded online, and reputations are trashed.

Gender change revelations

To help get the message to parents, online security specialist Tom Ilube was asked to investigate two mother and daughter pairings for BBC Learning's Share Take Care campaign. Armed only with their names and the town they live in, he spent a day checking what he could find based on information they'd shared in social media.

Forty-year-old Lisa Simpson from Manchester was not that surprised that the digital detective was able to dig out family details including her father's gender change.

But she gasped when Tom showed her a picture of her current partner in his underpants, which she had obviously forgotten about posting.

"That's only available to about a billion people worldwide," he told her.

Lisa and 16-year-old daughter Talia are big Facebook users and share pictures and status updates. Mum Lisa has more than 800 friends on the site: she claims she knows them all. She's a sociable lady. And open.

Before we filmed with her, she had no privacy settings on her Facebook account. But she has since updated them. "Why would I want strangers knowing so much juicy gossip about me?" she said.

But her main concern was that Tom had found out her mother's maiden name - often used by banks and others for online security.

"Often banks ask for it," said Tom. "The thing to do is not to use your real mum's maiden name. They don't care whether they use your actual mother's maiden name or something else. Just use something else that only you know,"

Lisa's daughter Talia already had privacy settings on her Facebook account but her jaw dropped at what Tom found on her Twitter account.

"Last year, you made a few end of the world confessions on Twitter. You might want to look and delete some of them," he told her.

Talia had also had personal chats with her mum over Twitter. "Were they not direct messages?" she asked. "No they were all public," said Tom. Twitter has a private messaging function which Talia is now aware of, and she has also taken down some of her previous posts from public places.

Tweeting the boss

Both 39-year-old community nursery nurse Sarah Fielding and her 14-year-old daughter Becky are keen Facebook and Twitter users in what they thought were their 'private' lives.

But Tom was able to find lots of their personal details like dates of birth, addresses and Sarah's mother's maiden name, her love of Man United and Robbie Williams. Nothing to be ashamed of, but again, useful to a potential fraudster.

How did Sarah feel about the information being publicly available? "That's quite scary actually," she said.

"To have got my full address, my previous address, my ex-husband, that's an eye-opener."

Daughter Becky was, if anything, more sensible with many privacy settings applied - but forgot her Twitter feed was public when she joked about how she did her homework - classic schoolgirl error.

Since our filming, passwords have been changed, accounts locked down to private, and potentially embarrassing online histories deleted.

And I'm being more careful too.

When I tweeted from the pub on a day off the other day, it never occurred to me that my boss was one of my followers, and he hasn't stopped teasing me about it, which is a bit embarrassing.

Tom has a brilliant tip: "Whenever you're about to post something online, pause and just imagine someone in authority, someone you respect, reading that post or looking at that photo. If that feels uncomfortable, don't do it."