Do they make mistakes on birth certificates?

I believe there has been an error on a birth certificate, obviously nothing can be done about it as all are long gone.

My great great grandfather Samuel Broome, born 1843 circa in Oldham's father was Joseph Broome b. 1811. This information has been found from the marriage certificate of Samuel and Hannah Hollinhead in 1866 and also from census.
The confusion lies with who is Samuel's mother. There is no record of a marriage of Joseph Broome before 1849 when he marries Alice Bardsley - yet Samuel and his sister Sarah are both born earlier than this.
There is a death of an Ann Broome in Oldham in 1848. So who is Ann Broome? Is she Samuel and Sarah's mother. The only way to find out was to send for the birth certificate of Samuel Broome.
What a surprise - it says mother Ann (nee Topp) but lists the father as Samuel Broome. Now either we have the wrong Samuel Broome, or someone wrote it down wrong and has mixed up father and son.
The only way around this is to send for Sarah's birth certificate (more money!) and see if Ann Topp is her mother.
Another mystery to solve. Keep you posted.!