Dead father on birth certificate

[Just Kia]

Possibly not an infant baptism? Maybe an older child? An adult?
Maybe the clerk/curate/etc forgot the mother's name?
I've come across a lot of baptisms (reasonably early on) that only list the father's name or at best father's name followed by "and his wife".

[Sloe Gin]

Even into the 20th century, it seems to have been usual for birth announcements in the newspapers not to name the mother, eg

"to the wife of John Smith, a son ..."

And presumably such announcements were placed by the family themselves, so no clerks or ministers to blame 

[danuslave]

Not really surprising.  Back then (and a lot more recently) a married woman was known as Mrs John Smith - no identity of her own at all.

I hope it's not still the 'correct' form of address - but it could be   

Linda

PS Mrs Elizabeth Smith would mean she was a widow