When he was first introduced in the manga, Law had tattoos on only four of his left hand's fingers. In the anime, all five fingers have a tattoo. Later in the manga, during the Marineford arc, all five fingers are tattooed as well.
Sabaody Archipelago Arc
Originally in the manga, when Law met Kid in the auction house, he notably showed Kid his middle finger. In the anime, this was censored with Law simply giving Kid a smug look.
When Law, Kid, and their respective crews encountered a Pacifista, it is not specified whether this one was Kuma or not in the manga and the scene ends with a cliffhanger. In the anime, this one was a regular Pacifista and the pirates were given some scenes fighting it. When it seemed that they defeated the Pacifista, it got back up and resumed its attack, essentially leaving the same cliffhanger as in the manga.
Law showing his middle finger in the manga.
The censored scene in the anime.
Law and his crew's interaction with the Kuja are also added in the anime. When they arrive on Amazon Lily, they enter the harbor with the Kuja ship only to be met with initial hostility by the Kuja islanders until Boa Hancock stops them. When Elder Nyon clearly states that men are forbidden on the island and the Kujas must uphold the law, Law and Jinbe manage to convince Nyon that Law is needed to treat Luffy's wounds. After forming a compromise, the Heart Pirates are allowed to dock at the bay.
During the Timeskip
In the anime, a flashback showing him sending the 100 pirates' hearts to the Marines is added. In the manga, this fact is only mentioned. This sequence contradicts Law's former bounty poster, which depicts him already wearing his new clothes before attaining his Warlord status.
In the manga, when Law confronted Doflamingo on the palace rooftop and was defeated by the warlord, he once again showed his middle finger. This was again cut in the anime, as Law only mocked Doflamingo without performing the gesture.
Translation and Dub Issues
When referring to others, Law adds ya (屋,ya?) to their name or epithet. In English, it can be translated as "Mr.", though ya does not denote courteousness and is generally used when referring to someone's profession. However, he has rarely used san to refer to certain characters, such as with Corazon and sarcastically with Vergo.
Likewise, there are different ways for his nickname coined for him by Luffy, "Tora-man", can be translated. It can possibly as "Tra-man", but is often subtitled as "Tra-guy" or "Traffy" in some media with said subtitles. The English version of Pirate Warriors 3 and Burning Blood instead localizes it as "Traffie".
Law's full name, Water Law, when taken together with his fight against Wellington, may be a reference to Waterloo, the place where, on June 18, 1815, final battle of the Napoleonic Wars was fought, which represented the ultimate defeat of Napoleon at the hands of the Seventh Coalition. The British commander at Waterloo, Arthur Wellesley, was the duke of Wellington.
Law's wanted poster shows Bepo appearing in the background with his head turned in the same position and stance as Usopp in Luffy's poster.
In the 7th Fan Poll, Law placed 5th, making him the most popular non-Straw Hat character.
In the 4th poll, he placed 10th.
In the 5th fan poll, he placed 2nd, making him the only character to place 2nd who is not Zoro, who has placed 2nd in every other poll.
Law uses the "smiley" style of Jolly Roger, as first seen used by his former superior Donquixote Doflamingo. But unlike Doflamingo's smiley, his does not have a "cancel" sign across it. The smiley most likely refers to the final moments of Donquixote Rosinante, who died with a smile before he told Law to remember him smiling from that day onwards.
Law's character song, which was released as a bonus song on the One Piece Log Collection - Sabaody CD is called "Dr. Heart Stealer". This is likely a reference to the hearts of 100 pirates he obtained in order to become a member of the Seven Warlords of the Sea or his ability Mes which he used to remove people's hearts from their bodies.
Law's escape from the attack on Flevance almost mirrors the actions of real-life pirate Francois L'Olonnais, who was shipwrecked and attacked by Spaniards. L'Olonnais covered himself in the blood of his crew and hid amongst their dead bodies in order to survive. Francois also famously cut out the heart of a Spanish hostage to intimidate the other hostages into telling him a safe escape route. This somewhat resembles Law's act of cutting out a hundred pirate hearts to become a Warlord.
Law's birthday, October 6, comes from his surname's Japanese trancription first syllable and his name's Japanese trancription since 10-6 can be derived from to-ro.
Law's name was taken with 18th century real-life English pirate, Edward Low. Law's apparently infamous cruelty echoes Edward Low's own reputation for violently torturing victims before killing them.