(at around 1h 16 mins) In the Theatre des Vampires, Santiago unties the string on the woman's shirt but just seconds before this it is seen already untied and she moves it to cover herself.
(at around 22 mins) When Louis kisses Widow St. Claire, he gets some lipstick stain on his nose and in the next shot it's gone.
(at around 53 mins) After Claudia cuts off her hair, she throws the scissors on the floor. But in the following scene, after she screams when her hair grows back, she walks out and you can see her holding the scissors in her hand again, and with them she leaves the bloody cuts on Lestat's face.
(at around 3 mins) In the very beginning, just before Louis begins his story, the shot from outside the window shows Louis' hair down. The next shot in the room of Louis' back shows his hair pulled back in a low pony tail.
(at around 20 mins) When Lestat teaches Louis the rat blood trick, Louis drinks blood from the glass and in the next cut to him the glass is completely clean, showing not even a drop of blood in it.
Three scenes show a sailing ship with hoisted sails while at anchor (on the river during the opening shot at Ponte du Lac) or at the dock (when Lestat first attacks Louis, and later when Louis and Claudia flee the city). No responsible sailing captain would have allowed that to happen.
After Louis becomes a vampire, his reflection is visible in a puddle of water in the cemetery: Although in Vampire mythology it is said that a Vampire cannot see his/her reflection, it is clear that in this adaptation a Vampire can see his/her reflection (In addition to the puddle, Claudia looks in the mirror after she has cut her hair and sees her reflection)
(at around 3 mins) At the beginning of the film, we see Louis in the window of the hotel. When the shot changes to the inside of the room, it is from behind Louis as he is looking out the window at the city. If you watch closely, you can see that what Louis is looking at is actually a still image rather than the actual city, as none of the cars' headlights or taillights move and none of the other lights flicker.
(at around 18 mins) After Lestat kills the tavern woman with Louis's help and replaces her head on the table, her eyelids move slightly.
(at around 1h 7 mins) During the fight after Lestat returns from his 'death' in the swamp, the rear of his shirt flies up revealing perfectly normal skin (as apposed to his badly decomposed face/hands).
(at around 1h 21 mins) As Armand and Denis (the boy with Armand) begin to walk out of shot, Denis looks straight into the camera.
(at around 1h 13 mins) Even considering the supernatural powers of vampires, and perhaps his hat was on real tight, when Santiago "dances" up to the top of the tunnel, his hair and cape should have fallen due to gravity.
(at around 9 mins) When the vampire Lestat first changes Louis he floats him above and drops Louis into the Mississippi. The ship beside Louis when he emerges is ironclad. The movie claims this happens in 1791, but ironclad ships did not come into use until the mid 19th century, with the famous Monitor v Merrimack marking a turning point from wood to steel in naval warfare.
Paris was surrounded by the German army on September 20th 1870, until January 1871 due to the aftermath of the Franco-Prussian War. This was an obvious danger after the defeat of the French army on September 2nd. No-one in Paris, however, seems to notice.
In 1988, as Louis is leaving the movie theatre, a first generation Ford Crown Victoria police car is seen speeding on the highway nearby, which wasn't produced until 1992.
The "no drinking dead blood" / "stop before the heart stops" rule of vampire feeding seems remarkably arbitrary. It would be difficult to classify the blood Lestat squeezes out of a dead rat - then offers to Louis - any other way than dead (he even remarks on its coldness), yet Louis drinks it with no ill effects - merely distaste. Also, Lestat twice offers Louis a glass of blood from the prostitute he tortures. Granted, she is still alive at this point, but if it is so important for the blood to be flowing in living veins, this is surely as much a violation of the rule as letting Claudia drain her freshly-killed victim dry, which Lestat insists on her not doing.
The vampires kill many city inhabitants in cold blood, including prominent store workers, seamstresses, and aristocracy, often right in their home. However at no point do the police ask them any questions or relatives seek answers for any of the deaths.
The census of 1805 put the population of New Orleans at ~10,000 people, including slaves.
With the vampires living there for 30 years from 1891 on, killing 3 people each night, they would have wiped out the entire populace in less than a decade.
Even accounting for passers by, population growth, and immigration influx, it still isn't remotely possible.
(at around 1h 45 mins) Louis tells his interviewer that he saw the sun rise for the first time in 200 years when he watched his first movie. It is implied that Louis saw the movie when it was new, or almost new, in the late 1920s, when he had been a vampire for less than 140 years.
Louis comes back to New Orleans (after years) to find a nearly mummified Lestat hiding in a graveyard. Right after the interview is broken off and the interviewer is riding off Lestat is in the back of the car; bites him and is back to his former glory instantly. A vampire drinking blood in the time Louis is in the old world would not be in this state.
When Armand is talking to Louis he tells Louis that he is the oldest "living" vampire in the world. The word "living" implies mortality and as vampires are immortal he surely meant that he is simply just the oldest vampire in the world.