Researching common names such as Smith, Jones, Williams, Brown, Green, Johnson, Miller, Anderson, Davis and Wilson are always difficult. The parameters of the search in some cases can be too enormous to develop a method to effectively narrow the possibilities. It does help in these cases to have an unusual first name and have an initial. However, many Mary Smith's have been found as have many John Williams'. It takes a lot more work but by staying organized and leaving yourself a paper trail you can be much more effective.
Discovering that some of your research material has falsified information can be disheartening. A few states changed the date of birth and the city, county or state of birth on the amended birth certificate so that it did not agree with the information on the original birth certificate.
Information given by the birth parents could be falsified and the non-identifying report would then not be a true background report. Some birthmothers used an alias name and the birth name that was reported on the original birth certificate was false. However, usually some of the information is true and in some cases there is enough truth in the information to still complete your search. Many times it is a process of determining, through the process of elimination, what information is true and what information was falsified.