When describing things or people that are old, is yaşlı used only for people and eski only for things? What is the difference between yaşlı and eski?  

Thanks in advance.

I think thats correct

I thought you were correct, but have since learnt otherwise.

Yaşlı is used (only) mainly with people (or things that are alive, like animals)

Eski is used (only) mainly with objects (on non-living things)

My genuine thanks to the Turks who have pointed out my error. 

I know from experience that you are correct. When I was in Turkey learning Turkish I think I referred to a person as "eski" and got a pretty strange reaction... 

 Yes eski adam means someone whose time is past like "last year´s man".

Or it means the previous one.

Ebru´nun yaşlı kocası: Ebru´s elderly husband

Ebru´nun eski kocası: Ebru´s ex-husband

What about "ihtiyar" ?

 That is elderly as in a person: ihtiyar adam. It is also used for a village elder.

There is also "antika" = antique, which you would only use for an object!

There is no strict rule saying "genç/yaşlı" is used for persons only.

It can also be used for things:

You can say "arabam yeni/eski"

You can also say "arabam genç/yaşlı" = "my car is young/old or aging"

genç dağlar = young mountains, yaşlı kıta = old continent, yaşlı bina = old building...

You can find many examples like these.

yes but you should stress that these are exceptions

you cannot just say yaşlı/genç for any object

it does NOT fit to many things

yaşlı bir elbise giymişsin!

evlerindeki genç halılar çok güzeldi!

by the way what is genç dağlar?

İ saw there is "genç kıvrım dağlar"