How many income producing real estate properties (single family and
multi-family units) are listed for sale at any given time in the USA?
... in the world?

I will guess 100,000 in the USA/ Five million world wide. The market
is actually larger but often income producing is neither mentioned nor
inferred in listed for sale anouncements. Getting an accurate number
is unlikely as several anouncements of the same property are typical
in the months/years preceding actual sale, and professional realtors
often are not involved until a buyer has been located by the seller.
Typically the closing documents do not state (or infer)income
producing. Often income producing is an option chosen by the buyer but
not the seller.  Fairly often the new buyer occupies the dwelling,
even though the previous owner used it as income property. USA laws,
beauracratic decisions and court decisions (regarding delinquent
tenants) have resulted in large losses to the owners of income
producing property, so rent and lease amounts are up to double what a
person would pay in mortgage payments if they bought an equivalent
property. The USA (and most other countries) market may not be
shrinking as the number of Americans with very bad credit is still
increasing.   Neil

Neil,
Thanks for the input.
I was hoping for more hard data, but your dialogue was both generous
and helpful.  Thanks.