This example is UK based and is based on a real event that happened this week.
So here goes.
Having looked on the General Register Office website https://www.gro.gov.uk/gro/content/ you find a birth entry that seems to correspond to the person you are looking for.
You then send off for that birth certificate, you receive it back, so now you have a birth date, the date noted was actually in the previous quarter (you have six weeks from birth to register it) and this birth was registered on the first day of the next quarter.
Entering this date on your tree (Ancestry as an example), you then get more hints, they confirm that it was the right year.
Another hint pops up, a baptism, different date and the names do not look right. So you go and investigate.
Their is an image, you check to see what it holds and find some errors in the names, some have changed, but it is in Latin, so they have used those given names.
You do not realise the biggest error, you just think, oh well it must be an error in writing up the entry. As the birth is the day after the baptism, per the birth certificate.
I bet you are thinking, that is enough evidence.
This is me now looking at the evidence, that was found.
Fact – a birth date has been found via a birth certificate, not reliable, the reason for this is that it was noted that when this person married they signed with an X, this might indicated that they could not read or write. So with this information only the year maybe correct.
Evidence – The Baptism record, the date of the baptism indicates that it is a Sunday https://www.timeanddate.com/date/weekday.html also looking above and the previous page I find more entries for that day, I also check the dates most of them are Sunday, but a couple are on a Wednesday, this is not uncommon in a Catholic Church (our current Prince George was on a Wednesday). They did say the address on the baptism was the same as the birth certificate. I then look slightly to the right and I see another date, I know a small amount of Latin and I think it says born (nata or natus), to confirm this I use Google Translate and yes I was correct. So this date is 19 days before the baptism and 20 days before the actual birth. I mentioned this to the person making the enquiry and they said they would keep to the birth certificate date and another person said the information on the baptism must be wrong unless you get in a time machine.
Hmmm, I wonder, did they use the day after the baptism as the birth date to avoid late charge fees, as they would have incurred them, if using the correct date. I have not found any more records to suggest which birth date they used.
So always look at the facts and make sure you analysis every bit of evidence you find, even if you transcribe the document yourself to give you confirmation.
Update 4 June 2017: If the entry in the Baptism Book, was wrong, how come the following pages are dated the month following the baptism and a month before the birth was registered, also written by different people who performed the ceremony.