I have traced a relative born in July, 1873. I know the mother died in child birth or shorthly afterwards. However, when trying to trace the mother's death, I have found only one "match"...however, it's before the child's birth. Is it possible the date of birth could be wrong?

Even though registration began in 1869 it wasn't enforced until the 1880's and even then not every birth, marriage or death was registered. Her death may not have been registered so don't assume anything unless you can back it up with other evidence. Check into cemetery, church & newspaper records to see if her death can be found there.