For those who is going to bring cash (USD or EUR).
Russian banks are very concerned about the conditions of banknotes in USD or EUR you want to change. Banknotes (EUR or USD) must be in immaculate conditions or so - no stamps, marks, tears, attritions etc., otherwise they refuse to change.
According to the law, there is no difference in rates for small and big banknotes and you can exchange foreign currencies only in the bank (not travel or money changing bureaus, shops, money changers as private persons, fine is 100% of the sum, but very rare applied). Sometimes bank branch or bank foreign exchange office is just a cubic kiosk but it’s OK. At the airports the rate is 20-30% below than in the city center.
At the moment there is no need for Russian people to seek for foreigners to buy dollars cheaper than in bank (as it was 15-20 years ago), since the spread between buy and sell rates in the banks is minimal, some smart guys (like me :) ) buy dollars in Moscow Stock Exchange at the interbank exchange rates with smth about 0,0002% commission and after 1 month on the account I can withdraw it in cash with no commissions. Paradise. Money changers in Russia disappeared many years ago.

In the second half of 2014- first half of 2015 when Russian ruble fell from 30 to 80 R per 1 USD and people were attacking banks for buying dollars, there were popular 2 scams in Moscow (especially around Railway terminals) and in the center of Sankt-Petersburg.

1. Was heavily widespread. You give money to a cashier, she returns it to you after a few minutes because of many reasons - her computer is down, the bank doesn’t have enough rubles or dollars for exchange, the office is about to close, the central office prohibited the operation etc. Of course part of your money is missing but you don’t count because you are in a hurry since your train is about to depart, you trust banks, you watched the whole process clearly and everything was ok. Variant – the cashier exchanges your money, counts dollars or rubles you buy manually or using the machine, everything is OK, you watch the process, you take money, don’t count, come home, count – part is missing.
You communicate with cashier through the bullet-proof glass and transfer money to the cashier through the metallic box - you slide the lid, put money inside the box, close the lid, the cashier open the lid, take the money, close the lid). Some smart cashiers put drops of glue or honey (!!!) on the side inside the box and while she/he is putting your money inside the box, she/he sticks 1 or 2 banknotes to the drops on the side of the box by the invisible gentle hand movement. If you count and find that some missing she always can say look carefully into the box.
I was told few stories when guys came next day promising big problems for the cheaters and they got the missing money back. But since it’s near railway terminal the most take a train and who knows when they come back.
The cure for that is very simple – Count money every time when you let money in or out your hands, even or especially if you watch the whole process clearly.

2. Less popular but happened. You give money to the cashier and she declares that one of the banknote is fake, calls the bank security, her chief and all of them are f@cking your brain that you would have a lot of problems with the police, will go to prison etc. and they have to confiscate this banknote, all your money for testing etc. Their goal is take some of your money and let you go. According to the law in this case, the cashier must call the police, the police come, fill up the protocol and, since you are not in the Interpol wanted list, let you go with no consequences at least for the first time.
Good idea is to copy or scan at home all you banknotes you want to change and be calm and firm. Call the police? Excellent! The cashier has replaced the banknote with a fake one is a good excuse.

Even though I’ve never heard about these scams since the end of 2015, you know WC is a special event that attracts bad guys. May be police will sweep all these artists out, may be the artists will buy the police. Life is a game.