You do not have to look far for an example. Take the notion that genealogy or family history is something that is done by old people after they "retire." The actual practice in the Church seems to support this notion or theory very well. It would be easy to become convinced that old people had some special interests or abilities lacking in the youth that gives them a predisposition to accumulating family history. This may also be a cultural issue that preserving family traditions is a function of age. But the anomaly is that there are a good number of young people involved in genealogy.
Another common notion, particularly among members of the Church with a long history of ancestors in the Church, is that "all my genealogy has been done." Even though this statement cannot possibly be true given the number of direct line ancestors and their descendants that each person is related to, this is a very persistent notion that I hear regularly. The anomaly is the fact is that there are presently at least two software tools that will help to dispel this belief or notion. First is the program known as Puzzilla.org and second is the newer Descendancy View in FamilySearch.org's Family Tree.
A very persistent notion is that somehow Temple work and family history (genealogy) are separate and distinct areas of concern. Active, Temple attending members often justify their inactivity in family history on this artificially imposed notion. It is more than just an anomaly that you do not have to go far to find statements from General Authorities and Prophets to answer this. Here is a quote from Elder Richard G. Scott of the Quorum of the Twelve Apostles:
Temple and family history work is one work divided into two parts. They are connected together like the ordinances of baptism and the gift of the Holy Ghost.The main idea of this persistent notion is that you can somehow separate and compartmentalize these two parts and ignore the family history part.
Yet another notion about family history is that it is a class during Sunday School time taught once or so a year. Many of the newly called Family History Consultants I have talked to during the past couple of years have told me that they were "called to teach a family history class." This notion flies in the face of the vast anomaly of the very detailed instructions to everyone in the Ward and Stake that are defined as involved in family history. See LDS.org Family History Topics. A few minutes spent looking at the responsibilities of each level from the Stake President to the Family History Consultant will quickly dispel that notion. When I visit Wards and ask about a family history class, they usually always reply that they "just had one" or that they might have one in the future.
There is also a notion that only certain members of the family have the genealogical responsibility. This notion holds that if my [fill in the blank, i.e. grandmother, mother, father, aunt etc.] is involved in genealogy then I have it made and don't have to do anything. The anomaly here is simple, family history and Temple work is an individual responsibility. Each of us has our duty to work out our salvation. See The Book of Mormon, Moroni 9:27
27 O then despise not, and wonder not, but hearken unto the words of the Lord, and ask the Father in the name of Jesus for what things soever ye shall stand in need. Doubt not, but be believing, and begin as in times of old, and come unto the Lord with all your heart, and work out your own salvation with fear and trembling before him.In fact, you might want to re-read all of Chapter 9.
I could go on, but I suggest that you go back to the LDS.org reference above and start finding out how family history is really supposed to operate and not just as an anomaly.