Several. Difficulty getting pregnant, miscarriage, chromosomal abnormalities, undergrown baby, diabetes, preeclampsia (toxemia), cesarean delivery, uterine bleeding before/at delivery, etc. These are more common after 40 than 35 some risks rise with age. Couples should consider these risks and costs and loss of income if problems arise. However, if spontaneous conception in healthy women, majority do well.
Risk goes with age. The risk of chromosome problems and spontaneous abortion go up with age. However the risk is not as high as many fear. For example, a 35 year old has roughly a 1/200 chance of having a baby with a chromosome problem. It goes up every year from there. The risk of cesarean section, high blood pressure and gestational diabetes goes up also. However the most likely outcome is a heatlhy baby!