Okay, not so fast!
I found this discussion and it made a whale of sense.
a)http://www.usingenglish.com/forum/threa ... -like-that
That is, with more than one item (things - generally things that can of different makes, types, brands, etc) you would use "things like those".
Thinks "like that" to one-item thing, and (it seems) when you are talking in a more or less abstract way. For example, to complaint about things, to talk about things in general. As in a general remark/commentary.
b) I developed one theory of my own, that is:
One way to set them apart, would be testing them for "one of those things" (if you can replace it, and think of it as being in a set of two pieces or more). Read on...
In your piece ""In city We have lots of things to do. We can go to the movie theater, we can go to malls and do a lot of things. In the countryside, however, we don't have things like that
"" -to change the highlighted part by "we don´t have of those things" would seem unnatural, not advisable.
c)One of the senses of "like those'', though; is to think of it as an abstract thing, wich you can´t talk about it "in a specific way", similar (but not quite the same way) to the notion explained in  and [a].
It´s a special case, anyway you can´t replaced by "like that".http://www.macmillandictionary.com/dict ... tish/thing
It may be a case of "practice makes perfect", people have to live with looking up the expression, almost on a case-by-case
grounds, until get used with its usage.