Mistakes in Farewell Tawaf
Question

What are the mistakes that some pilgrims make during the farewell tawaf?
Praise be to Allah.Tawaf: The last action of Hajj
Shaykh Muhammad ibn ‘Uthaymin (may Allah have mercy on him) said: 
“Ibn 'Abbas (may Allah be pleased with him) said: “The people were commanded that the last thing they should do in Makkah was to circumambulate the Ka’bah, but an exception was made for menstruating women.” (Narrated by al-Bukhari, 1755; Muslim, 1328) 
Mistakes made in Farewell Tawaf
So tawaf should be the last action of Hajj that a person does. 
People make several mistakes when performing the farewell tawaf : 

Some people do not make tawaf the last thing that they do, rather they go down to Makkah and do the farewell tawaf when they still have to stone the jamarat, then they go out to Mina and stone the jamarat and then leave. This is a mistake and that does not suffice as the farewell tawaf in this case, because it is not the last thing that the person does in Makkah, rather the last thing that he does is stoning the jamarat. 
Some people do the farewell tawaf and then stay in Makkah after that. This means that their farewell tawaf is invalidated, and they must do another one when they are going to leave. But if a person stays in Makkah after doing the farewell tawaf in order to buy something or to load his luggage etc, there is nothing wrong with that. 
Some people, when they do the farewell tawaf and want to leave the Mosque, walk backwards, saying that they do not want to turn their backs to the Ka’bah. This is a bid’ah (innovation) which was not done by the Messenger of Allah (peace and blessings of Allah be upon him) or by any of his Companions. The Messenger of Allah (peace and blessings of Allah be upon him) venerated Allah and His House and if this were indeed an act of veneration towards Allah and His House, the Prophet (peace and blessings of Allah be upon him) would have done it. The Sunnah is, when a person has completed the farewell tawaf, to leave the Mosque walking forwards, even if he turns his back towards the Ka’bah in this situation. 
Some people, after doing the farewell tawaf, stop at the door when leaving the mosque and turn to face the Ka’bah, as if bidding farewell to it, and they make du’a or say salams and so on. This is also a kind of bid’ah, because the Prophet (peace and blessings of Allah be upon him) did not do that. If it were something good the Prophet (peace and blessings of Allah be upon him) would have done it.

And Allah knows best.