Do you see any passage that suggest "authorial intervention" in Chekhov's the lady with the pet dog? If so, explain the purpose and the effect of such intervention.

A nicely subtle question. I would say that yes, there is authorial intervention throughout the story. It doesn't show up in any sudden intrusion (the author does not, for example, address the reader directly). Instead, it shows up in some of evaluative/descriptive comments that shade the story. For example, consider the following lines:
She read a great deal, used phonetic spelling, called her husband, not Dmitri, but Dimitri, and he secretly considered her unintelligent, narrow, inelegant, was afraid of her, and did not like to be at home.

To add "secretly" adds a shade of authorial intrusion, because this is talking about his (Dmitri's) thoughts.

A more marked example is found here:
The stories told of the immorality in such places as Yalta are to a great extent untrue

That's the author speaking directly.

As for the effect, such statements produce a sense of the author controlling things, a sense of distance, and try to guide the reader's response.

Greg