(at around 15 mins) We see a shot of the Royal London Hospital in Whitechapel. However, it only gained its "Royal" status in 1990 - for the duration of its previous 250 years history, it was called just The London Hospital.
(at around 1h 17 mins) Inspector Abberline explains to Mary Kelly that they should pass notes via the barkeep of a nearby inn. "Barkeep" is an American usage; in England it would be "barman" for someone working in the pub or "landlord" for the owner.
(at around 48 mins) When Abberline first meets, and discusses the Ripper killings with Sir William Gull, Abberline's drawing of a Liston knife keeps changing shape and position on the blackboard between shots.
(at around 41 mins) Upon arriving at the murder scene (in the back yard of a house), Inspector Abberline's coat and hat are clearly hung upon the fence a moment before we see him actually hang them there.
(at around 8 mins) When men broke into the room where the couple was having sex at the beginning of the film, the woman quickly covers up her bare breasts with her sheets, then during the close up of the man, she is again trying to cover her breasts.
The film depicts the Ripper in his carriage en route to pick up his next victim (as depicted in the next shot) racing along the Thames with Big Ben and the Tower in the background. This would mean that he was on the wrong bank of the Thames, racing away from the Whitechapel district, which was located within easy walking distance of the Tower.
(at around 1h 10 mins) A little after the second murder, Abberline is talking with Gull about "Jack the Ripper". However, he was not to become known by that name until the double event murder and receipt of the "dear boss" letter, almost a month later.
Liz Stride would not have been able to see the reflection of the killer's knife in the puddle she was bent over because the killer was coming up from behind her. She could have only seen the reflection of something in front of her, or slightly to the sides.
By the late 1800s glass windows were becoming common, and while the glass was heavier and sometimes uneven, it was certainly clear and very much like modern glass (although more expensive). While still produced by a glass-blower, it could be blown into large sheets and cut for windows. Thus the modern-looking windows in the movie could have been around in 1888.
The goof items below may give away important plot points.
(at around 1h 35 mins) When Inspector Abberline is hiding a small gun behind his back when he is about to confront Dr. Gull you can see a tattoo on Abberline's finger. Tattoos were around but not on fingers of respectable police officers.
(at around 17 mins) When Ferrall is performing the lobotomy on Anne, on the last tap we cut to Gull talking. In the glass we see the reflection of Ferall performing the tap, but there's no sound. In the following shot of Ferrall he repeats the tap this time with sound.
Inspector Frederick Abberline is depicted inaccurately as a young man who is an opium addict and psychic as well as dying soon after the Ripper murders. The real Frederick Abberline was a middle aged man in 1888 with no known opium addiction or claims of paranormal ability. He lived until 1929 when he died in England. An alternate ending on the DVD has him living to old age, which is accurate, but sets his death in Hong Kong, which is not.
(at around 1h 20 mins) It is stated that the infant son of Prince Albert-Victor and Ann Crook is a Prince and heir to the UK throne. This is incorrect as they were married by a Roman Catholic priest, and the Act of Settlement (1701) specifically forbids Catholics from holding the throne or claiming marriage to Royal family members. Prince Albert-Victor could stay in the line of Royal succession only by disowning his wife. The son would not be a Prince or eligible for succession unless Parliament passed a special vote to adopt him into the system. Real life analog: Prince Michael of Kent and his family.
As in most film versions of the Ripper murders, the Ripper's victims are shown as being considerably younger and more attractive than in real life. In reality all of the Ripper's victims were in their mid forties and not very good looking, except for Kelly, Mary Jane. No authentic likenesses have ever been found of the women when they were alive. The only known photographs are of their mutilated corpses.
(at around 1h 35 mins) When Abberline takes out a gun and points it at Gull, Ben Kidney hits him from Abberline's front-right side. In such a large room with plenty of empty space to his right, there's no way Abberline would have not seen Kidney coming at him (in the kind of distance covered by him from the Fire to Gull)