Corrections in red.  Stylistics in blue.

About People in the Metro

I like observing people in Moscow's metropolitan while they are taking a nap (or "snoozing [1]. It's always some bouts [2] of fun! There are old people, weirdos, alcoholics, young mothers, youths, and so on and so forth. Someone is returning back home after a party, someone is on the way to work, and someone just has nothing else to do. It's amusing when you notice a person who is tilting to one side, losing consciousness, or struggling with a drowsiness.

Psychologists say that you can see someone's real face when he is sleeping.

I snooze in the metro as well. I think the underground has some kind of magical influence on people. You can fall asleep there in the train even you've just had a cup of coffee.

[1]  "take a nap" is not wrong.   But that makes it sound like the person's goal in entering the metro system is to go to sleep for a while.  If you say "snooze," it sounds like a tired person simply falls asleep without really intending to.

[2]  I don't understand the use of the word "bouts" in this context.

Very well written and amusing.