Please give us an example.
Where do I start? Just about everything! The more more I learned, the more holes I saw through her story. The usual list of alleged 'differences' comes to mind, many of the quotes, statements passed off as fact that were really either only speculation, exaggeration, or from sources with very shaky ground.
For example, let's start with the famous and oft quoted line 'she knew things only the real Anastasia could have known!' This is stated as fact on many websites and by many individuals to explain why they believe in her. But taking this apart, we see in reality, there was nothing only the real AN could have known, and if there were, who would be there to verify it? Everyone in her immediate family was dead. If it was something others around the family could have known, then there's a possibility that one of those who fled Russia could have told AA, either intentionally, or incidently in conversation during one of their visits.
Perhaps the biggest one of these to me was the "Uncle Ernie's visit", usually referred to by AA supporters as 'dropping the bomb' or 'spilling the beans.' It's used to make excuses why Ernie was so out to get AA, apparently, so anxious to get rid of her that he conspired with detectives and newspapers to fabricate the FS story and falsify evidence (according to some AA supporters) Besides the fact that said trip likely never happened, or that someone else possibly knew about it to tell her if it did, the biggest epiphany moment came when I saw a German girl on another forum post, quite innocently and in a context not even concerning AA, that she had purchased a book called "In the Face of the Revolution". Published in Germany in 1922, it alleged Ernie took the trip and gave supposed 'evidence' to prove it. Since it did exist in Germany 3 years before she made her accusation to Ernie, the fact that the story was not unique to a member of the Imperial family, it really diffused the old 'bomb!'
AA supporters have openly stated matter of factly that FS was 5'6" while AA was 5'2". When I researched this further, I found out the only 'evidence' of FS's height came from the Wingender sisters, who said she was 'a little taller than us' and they were 5'3". The only other source of her height was that a foreman she used to work with guessed she was 'about 5'4". Yet as it passed around the net, the difference grew 2 more inches. Even the estimate of 5'4" is just a guess- if you're tired of my dirty dog story, do you remember the story of the group of fans who all met the rock star on the same night, yet all reported him a different height and all swore they were right? Height is very, very subjective, can easily be distorted in the mind's eye over time, and a person's perception of height can too easily be influenced by hairdos, shoes, them or the other person standing on a curb, incline or decline in the ground, curbs, steps or other factors. Bottom line- it's not a FACT that FS was taller than AA, just an estimate based on guesses. Same goes for the hair color accounts which are subjective and change from person to person. Might as well throw the old shoes in here, too, since people can get shoe sizes wrong, and sizes vary so much due to makers and materials.
Then take the claim that 'lots of family members who knew AN real well swore she was Anastasia'. As I checked into this, the details emerged- there were no 'close family members' on the list, and the people who claimed her didn't know her nearly as well as those who had denied her, and some who claimed her later denounced her. Others put on the list of accepting her actually made very different declarations I found elsewhere. Some who accepted her never met the real AN, and/or only based their acceptance on such intangibles as 'she has the tsar's eyes' or 'waves like the empress' or 'raised her hand to be kissed like a true lady of breeding.' A lot of it was generic perceived family likeness or random "Grand Duchess" in general, not much specific to Anastasia herself.
I could go on and on and on, but the post will only hold so many words.