How did Maximus become a slave?

Rather than quoting from serious academic articles, I'm going to use some simple educational websites. The History Learning Site states:

Who were slaves? They were people who were frequently captured in battle and sent back to Rome to be sold. However, abandoned children could also be brought up as slaves. The law also stated that fathers could sell their older children if they were in need of money.

Similarly Spartacus Educational explains:

Slavery existed in Roman society from an early stage of its development. There were several ways you could become a slave in Rome. Some became slaves because they could not pay back the money they had borrowed. The government would also take people into slavery if they could not pay their taxes. There were also many cases of poor people selling their children as slaves to richer neighbours.

So Roman citizens could technically become slaves (although it would be unlikely to happen at his age).

In the film, he had a home, but it was burned to the ground and his family left dead. At this point, his previous "life" is effectively done and he is now an unknown nobody. Except for the tattoo.

In the movie, the tattoo (SPQR: Sen?tus Populusque R?m?nus ("The Senate and People of Rome")) is on his upper arm. Vegetius (ancient Roman historian) confirms that soldiers were often branded, although he stated it could be on their hands to make it even more obvious if they had deserted. The punishment for desertion was Fustuarium (being clubbed to death). It does appear logical that, in the film, the slave owners who found and identified Maximus would have realised they could have lost a lot of money on a valuable slave if that had happened to him.

However, having said all that, it is worth remembering that it made for a fantastic story and so historical accuracy was not high up Ridley Scott's list of priorities. For more information on this, just check out this link which lists a large collection of the historical inaccuracies prevalent in the film.

Well due to the tattoo on his arm they thought he was a deserter and he refused to give them any information about himself to explain otherwise.

Any historical inaccuracy at this level of detail should probably be written off as a convenience of the story telling (like the flaming ballista bolts in the opening sequence etc.).

Even if it could be definitely proved that becoming a slave in this way this would have been completely impossible, how many of the audience would know and, out of them, how many would care?

IIRC, he was found, half-dead, by a slave trader and sold into slavery. By the time he was discovered to be a free man, he was too valuable to his owner because he had already gained notoriety as a Gladiator. I believe by that point he enjoyed the spoils and adulation a winning Gladiator received, and since his wife and son were already dead he has nothing else to live for.

In the movie, by the time he is picked up by slavers, he's spent. His wife and child are dead, his land destroyed, and he is close to death himself. After his recovery he is sold as a slave, Proximo mentions the tattoo and the slaver says he is a deserter. He doesn't fight at first because he is tired for working for others and doesn't care. He fights in the arenas because it's life or death, unlike the wooden sword tryouts.