Lord McAlpine has vowed to go after Twitter users who wrongly linked him to child abuse allegations following a botched BBC Newsnight investigation.
Lawyers for the Tory Peer have warned they are using technology to track people down and seek "settlements".
The Commons Speaker's wife Sally Bercow is among those being targeted.
some of the comments on Twitter were forwarded, or retweeted, more than 100,000 times.
Lord McAlpine's lawyers insist they know everyone who used his name - and if people do not come forward to reach an agreement first, they will be chased down.
Scotland Tonight looked at the situation, and discussed it with social media consultant Craig McGill.
More About Scotland Tonight
- STV looks at what will happen if Scotland votes No to independence
- Scotland Tonight: Nicola Sturgeon and Johann Lamont head-to-head
- Alistair Darling quizzed on pledge of more powers after a No vote
- Alex Salmond grilled on cost of corporation tax cuts after Yes vote
- Ed Miliband urges Labour voters to 'show solidarity' and vote No
- Forth Road Bridge celebrates 50th anniversary with festival of events
- Church of Scotland: 'Respectful dialogue' needed in referendum