It is more common all the time for women who are slightly older to conceive and give birth to healthy children. The risks for miscarriage are generally higher, especially if a woman has previously had children at a younger age. There is also increased risk of premature birth or slightly lower birth weights, but medical technology in dealing with those difficulties has advanced greatly in the last two decades. Pre-natal nutrition and avoidance of the use of cigarettes, alcohol and drugs, while important at any age are even more important as a woman ages if she wants to have a healthy baby.
In most cases, women in their 30's, mid 30's, or even 40's can and will have healthy and safe pregnancies. I had my child at age 34 and had no unusual problems. I know some people who had their children when they were in their late 30's and one person was even in her mid 40's. Many celebrities are carrying twins and they are in their 40's and have healthy pregnancies as well.
Increasing age pretty much negatively affects everything is life, so thus, pregnancy will be no different. But I stress that healthy pregnancies over age 35 are extremely common and likely these days.
Increased problems during pregnancy due to age: Down syndrome, chromosome abnormality, Autism
The main concern with a child being born to a mother over 35 is an increased risk of birth defects or chromosomal anomalies (such as Downs Syndrome that was mentioned in post 2). Often, mothers in this age group are offered extra screening tests like an amniocentesis. These tests themselves are a risk to the fetus, but they are often thought necessary.
The mother's health can also pose a threat to the pregnancy. The older the mother is, the more likely she will develop certain pregnancy complications. Some of these complications, like preeclampsia, can cause premature labor. Other complications carry their own risks for the fetus as well as the mother.
To begin this discussion let's take one danger that is common knowledge and one that is a bit more controversial. The former is the chance that the child will be born with Down's Syndrome. I should clarify, though, that this possibility doesn't begin to increase exponentially until the young lady reaches the age of 35. However, it still is one of the "potential dangers to the developing fetus" for a mom who is over thirty. The latter is an increased possibility of autism. The age of the mother is not a proven factor, mind you; however, doctors are beginning to discover a correlation between a mother's age and a child eventually diagnosed with autism.