Birth dates, especially those determined from Census records can be out.
Hand written records can also be very difficult to decipher and or transcribe.
When researching it is also always good practice to view the original document be it a scan or microfische rather than taking a transcript as gospel.
Whilst Certificates are supposed to be accurate, that is not always the case. Lies have been told to the Registrar and the Certificate can have the wrong parent(s) declared, voice of experience here, been there found that
As you are new to Genealogy, can I suggest that you look at the Pros and Cons of taking a DNA test, but be prepared for the downsides. That said what could be worst, spending years researching only to find via a DNA test that your Family Tree is not a valid Biological Family Tree.
Good luck with your research.