Here is what I found after some search in Russian/Ukrainian internet.
Apparently one inaccuracy is that in the main version (which is in Peterburg, this is actually the 2-nd version, and most famous because it was purchased by the tsar for the enormous price of 35 thousand roubles), several
cossaks are smoking pipes.
Actually a pipe is a traditional attribute of a floklore cossak in popular imagination.
The problem is that smoking probably did not exist in Ukraine at the time of the events shown in the painting. In the painting cossaks are writing a letter to the Turkish sultan Mehmet IV, and this is supposed to be 1676. Smoking was introduced in Russia by Peter I in the very end of 17th century, and there are documents showing that ukrainian cossaks did not smoke even at the time of Peter I.
(Repin worked on this paining more than 10 years, dong a lot of research, traveling,
and using a private museum collection for cossak artifacts. But perhaps those items were not properly dated).
In the latest version of the painting (that which is in Kharkov) no one is smoking.
The left-most figure on the Peterburg version is a young person filing a pipe.
The model for this figure was Repin's own son. But on the Kharkov version he removed it.
Actually, I don't know how much this criticism was justified because the habit of smoking could be taken by cossaks from Turkey, not from Russia. And I do not know exactly when the Turks started to smoke pipes.
Let me also add another historical inaccuracy: the whole inspiration for creating this painting was a "Letter of Cossak atanman Sirko to Mekhmet IV" which was published at that time and which Repin read. The letter is using very obscene language, and this is what makes them laugh. It is a general agreement that this later is an 18-th century fake.
And in general it is unlikely that cossaks would write an obscene letter to the Turkish sultan. But probably this was not the point of the criticism at the time of Repin.
All three versions of the painting can be seen here:
Remark. All the above is only my conjectures, based on the fact that on the later version of the picture no one is smoking. Chronology of smoking shows that it was known at the time in both Turkey and Russia but banned in both countries (death penalty). However these bans could not apply to Ukrainian cossaks.