Can taking too many tums (calcium carbonate) during pregnancy cause aging of the placenta, or calcify the placenta?

No: Not that I know of. Granted there is calcium in Tums, but a lot of women take calcium in pregnancy and, for the most part, your kidneys are going to filter out and pee out, excess calcium. Having said that, it's always possible to overdose on any medication, so I would not take more than is recommended. If Tums isn't helping your gastric reflux, then consider taking Zantac (ranitidine) or Pepcid.