1. Getting the titles wrong. Lady Sarah Winchester isn't the same person as Lady Winchester is, and when the author gets it wrong, it's easy to dismiss the story entirely.
(Here's the skinny on how to handle dukes ... marquesses ... viscounts ... barons ... and baronets.)
2. Getting the succession wrong. Inheritance of money is one thing, titles are another. Illegitimate sons could not inherit titles, period. Oldest sons could not be bypassed in favor of younger ones. Daughters could not pass along titles at all (there are a very few exceptions, by royal decree).
3. Getting the geography wrong. London to Gretna Green is 320 miles. Even if you figure an average speed of 10 miles per hour for a team of horses (and that would be tough to maintain over time, what with having to stop to change teams every few miles), it was impossible to do the trip in a day, much less overnight, during the Georgian or Regency eras. Which was the entire point, of course, since by the time a couple had been together and alone for such a long journey, the girl's reputation was ruined and irreparable.
4. 21st century characters who turn up in historical time periods. I don't mean modern-day characters who time travel. I mean people who were supposedly born and reared in the 1300s, or the 1500s, or the 1800s, but who think and act and talk and behave as though they just stepped out of Starbucks holding a latte and an iPhone, complete with modern sensibilities and politically-correct attitudes.
6.Trusting other authors to get it right. I swear I’ve read a historical novel where the hero complained about the heroine feeding him pablum – but when I checked, I discovered that particular baby formula was invented in the 1930s instead. Oops.