As a result of this natural decay of eggs, as women approach their mid to late 30's, they are more likely to have children affected by chromosomal abnormalities (the most common being Down syndrome). The "American Family Physician" article on Down syndrome provides the following graph showing the risk of Down syndrome as a % versus maternal age. As the article notes, from age 20 to 30, the risk of Down syndrome stays relatively stable, although it does increase somewhat. After age 30, the risk increases exponentially each year.
Additionally, women in their mid to late 30's are more likely to have miscarriages. The "Advanced Fertility Center of Chicago" provides the following summary of miscarriage rate by age group:
It is important to note that these rates of miscarriage only apply to pregnancies that have been confirmed by ultrasound, so the actual rate, including pregnancies lost very early on, would be higher.
To see this information interactively, check out the Age and Fertility Calculator.