FIRST, some genetic diseases:
Downs syndrome happens when you have too many of the 21st chromosome, and this happens when one chromosome doesn't separate at all during anaphase I in meiosis, and an extra chromosome gets pulled into the daughter cell. Your chance of it happening at 35 is 1 in 153, and 1 in 66 at forty. I'm guessing literally everyone mentioned this disease so moving on--
Edward's syndrome is the same, except the multiplied chromosome is number 18. People with this genetic disease don't tend to live very long, with the upper range being 2 weeks. Females with this disease tend to live a bit longer, however. The chance of having edward's syndrome is, at base, 1 in 5,000.
Not all genetic disorders are super harmful. Klinefelter syndrome happens when you have too many X's in a boy. Its rare, and doesn't usually do much more then make them infertile. Some learning problems pop up occasionally, but like, that's not so much different then having a kid with ADHD.
(Bonus, if you are missing your father's sex chromosome completely, you get turners syndrome, but that has nothing to do with the mother's eggs/pregnancy)
Though, not all genetic disorders such as these need to have genetic predisposition for it to happen, (its just a splitting mistake, after all. Those happen anyway.) being related to someone with a history of any of these will increase your chances.
Here in the the USA, it is not uncommon to find people starting families at thirty. My mom and dad insist that to try to do so beforehand would be foolish, because a person's's brain only completes it's impulse control development at thirty. Because of this, not all children will be born before 35. To be clear, I am not having children. I am adopting. But if I did, it probably would be after 35. Less then a 3% chance is NOT worth a hasty marriage, or a family built on it.
35 isn't some magical age where suddenly everything gets worse. Its getting worse every time your ovum divide. Having kids at 30 isn't much better, y'all.
And a way of skirting this issue entirely is to simply save and freeze an egg before you hit that age. Or like. A few eggs. And then mix that with your husband's, or female partner's stem-cell-turned sperm in a petri dish and insert it into the uterus. That way you don't even have to have sex.
Johnson SB, Blum RW, Giedd JN. 2009. Adolescent Maturity and the Brain: The Promise and Pitfalls of Neuroscience Research in Adolescent Health Policy. J Adolesc Heal. 45(3):216–221. doi:10.1016/j.jadohealth.2009.05.016 From https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892678/
Chromosomal conditions | March of Dimes. [accessed 2020 Feb 16]. https://www.marchofdimes.org/baby/chromosomal-conditions.aspx
Trisomy 18 (Edwards Syndrome): Symptoms, Life Expectancy & Facts. [accessed 2020 Feb 16]. https://www.medicinenet.com/trisomy_18_edwards_syndrome/article.htm#what_is_trisomy_18
Risks of Pregnancy Over Age 30. [accessed 2020 Feb 16]. https://www.stanfordchildrens.org/en/topic/default?id=pregnancy-over-age-30-90-P02481
https://en.wikipedia.org/wiki/Egg_cell, of course.
annnnd
Klinefelter syndrome | Genetic and Rare Diseases Information Center (GARD) – an NCATS Program. [accessed 2020 Feb 16]. https://rarediseases.info.nih.gov/diseases/8705/klinefelter-syndrome/cases/31312