So I am watching Mankind the Story of All of Us, and in the 3rd episode it describes Roman gladiatorial games.
The documentary claims that the Gladiatorial games were free for everyone to watch. It also depicts women in the spectators. How historically accurate are these two things?
I will answer the first question
the Gladiatorial games were free for everyone to watch?
Not really, quoting from Wikipedia (I don't know how to re-write it in my own words so I'll just paste it)
Towards the end of the Republic, Cicero (Murena, 72–3) still describes gladiator shows as ticketed — their political usefulness was served by inviting the rural tribunes of the plebs, not the people of Rome en masse – but in Imperial times, poor citizens in receipt of the corn dole were allocated at least some free seating, possibly by lottery.[165] Others had to pay. Ticket scalpers (Locarii) sometimes sold or let out seats at inflated prices. Martial wrote that "Hermes [a gladiator who always drew the crowds] means riches for the ticket scalpers".
The book "Those About to Die" by Daniel Mannix (Panther 1960) relates that women were among the spectators, including
...noble ladies on the podium [who] often lost their heads. When one handsome young Myrmillo, only a few weeks before a simple farmboy living on the slopes of Apennine, paraded before the podium with his bloody sword upraised a great lady screamed uncontrollably and flung her brooch and necklace into the arena. Then she stripped off her rings, tossed them onto the sand, and finally ripped off her undergarments and threw them also. When the young Myrmillo came on to the crumpled garments, he thought that the lady had simply thrown him her scarf or cloak. As he picked up the clothing to toss it back, the underwear unfolded. The simple boy stood gazing horrified at what he was holding. Then he dropped the garmnents and fled from the arena "more terrified of a woman's underwear than he had been of his enemy's sword." The crowd thought this was killingly funny and nearly died laughing. The patrician lady's husband was not so amused.
Op. cit. p.122.
Games were not normally free. Sometimes emperors would sponsor events as a way of winning popularity with the public. Julius Caesar was, I believe, the first to do this.
Late in the empire the emperor subsidized games out of the public purse.
Women did attend. The Romans had no problem with women appearing in public. In fact, not only did women attend, sometimes well known free women actually fought in the arena for money or fame, even though it was considered "disreputable" to do so.
--- UPDATE
Fine. Force me to be the professor. Reading materials for the student:
The Story of Civilization volumes 4 and 5 have articles on Roman gladiatorial games.
Encyclopedia Britannica volume 11, article on gladiators
Among modern works is "Gladiators and Caesars: The Power of Spectacle in Ancient Rome" by Eckart Köhne, Cornelia Ewigleben, Ralph Jackson. In this book, it proves my point that entrance money was charged in many cases on page 20 where it says:
[Private organizers] derived high profits from the entrance money...
As it says in the answer above, even when the games were "free" because some famous person like Caesar was paying for them, there were still tickets required and those tickets were resold by scalpers, thus making the "free" event actually quite costly to attend.
