How many molecules are there typically in items made of plastics?
The short answer is a very large number and far more than you could reasonably count

Polymerization reactions typically produce very large molecules but not so large that a single molecule would make up as much material as a whole plastic bag or item of any significant size. This source on LDPE tells us that the typical molecular weight of the industrial product is 90,000 (some polymers are much bigger than this). 

For non-chemists molecular weights are (simplifying slightly) the weight relative to a single hydrogen atom. Carbon is 12 on this scale and ethylene (the monomer from which the plastic is made which consists of 2 carbons and 4 hydrogens) is 32. This mean that a typical molecule of the plastic is (crudely) made from a little under 3,000 ethylene molecules. The other fact you need to know is that there are about 6 x 1023 hydrogen atoms in a gramme of hydrogen (see the wikipedia definition of Avogadro's number). Simple mathematics tells us that a gramme of LDPE will contain roughly 6.7 x 1018 molecules so that is the order of the number in small plastic item which, I expect, weighs just a few grammes.

So, the bottom line is that even in a small plastic item consisting of a long chain polymer (LDPE is relatively short but other polymers might have chains 10-100 times more at most) there will be something like 1016 to 1018 molecules of polymer, which is a lot.