According to
Legacy Family Tree some of the top genealogy mistakes are believing family myths, believing that family trees online are accurate, thinking that people with the same name are the same person, and believing that all original family records are accurate.
When I first started researching my family history, I made some of these mistakes, and had to go to a lot of work later to correct them. I have also corresponded with people researching lines that are connected to mine, and learned that many of them have run into problems as a result of mistakes like this.
For many people, the family legend that they have Native American ancestry is a source of pride. Many families think they are descended from, or closely related to, certain well-known historical figures. Others have an interesting but undocumented story about an ancestor's adventures, achievements, or crimes.
The origin of these stories is usually unknown, but they have been passed along for several generations, and are accepted as true. Until someone starts looking for proof and discovers that there is no truth behind the myth.
Now that DNA testing has become accessible, it is fairly easy to find out something about one's geographic or ethnic background. In some cases it is also possible to use DNA information to find living relatives who can provide important information. Other beliefs need to be tested through careful research.
Unfortunately, many people post family trees online without checking to see whether they are true. They may have believed an old family myth. They may have copied their information from someone else who didn't do accurate research. They may have connected people with similar names who aren't really connected. They may have accidentally inserted typing mistakes which then get copied and perpetuated by others. In some cases, they haven't even applied basic logic (such as listing someone with a death date before their birth date).
When using family trees or anecdotes posted online by other people, take a good, hard look at their sources. Did this information come from reliable sources? Can you reproduce some or all of their research. If they don't list sources, it's better not to use the information unless you can verify it yourself.
This one can be crazy-making. It's not at all unusual to find several people with similar names, all about the same age, all living in the same area. Even a name that seems very unusual may have been used by more than one person. Sometimes cousins will have the same name because they were named after the same ancestor. A nephew may have been named after his uncle. Just checking to see if their parents, spouses, or children also had similar names doesn't always help. It's not that unusual to find several men named William or John who were the sons of men named William or John, and who all had wives named Sarah or Mary. I've seen cases where people thought a father and son were the same person because they had the same name and married women with similar names. I found one instance where a woman divorced her husband and married his father, who had the same name!
It's important to take discrepancies seriously. Different birth dates, different professions, different family structures -- any differences at all should be thoroughly investigated before assuming that this John Smith is really the same as that John Smith.
Family Bibles are often seen as authoritative sources for information. Often they are. But in many cases they are inaccurate, because the person recording the information made mistakes. Often, events like marriages and births were not written down as they occurred, but were listed much later, from memory.
People sometimes write the wrong dates (or even the wrong names) on the back of photos because they are working from a flawed memory -- or just guessing. Marriage and birth announcements sometimes have intentionally fudged dates. Letters are prone to all the same mistakes (and sometimes deliberate deceptions) as anything else. Death certificates contain information supplied by informants who may not really know what they think they know. Even grave stones have been found to have wrong information carved on them.
Again, research is the key. Compare family records with official records, and compare several different sources with each other.