Is there any way to predict foundation problems?
Outside of naturally occurring activities like earth quakes, sink holes, etc., I'd say the current condition relative to the age is a good indication of what's to come. 

There's no real answer to this without inspecting the foundation.

An old, well built foundation that has never had problems and shows little sign of damage (cracks, crumbling, staining, holes, etc.) might last 100 years longer if maintained.  A 5 year old foundation that was poured sloppy and has had water seeping in since day one is more of a risk.

A home inspector would be able to give you a good opinion as to the quality and current state of the foundation.

You could also ask some neighbours with similarly aged homes what their experience has been.

Beware of something that looks too good for its age. It's unlikely something 100 years old wouldn't have cracks or some water staining.  If it's been repaired, the quality of the repair needs to be looked at to ensure it's not just a façade someone put up to sell the house.  A good quality repair on an otherwise intact foundation wouldn't be a huge risk in my opinion.