When Lara reaches the boat at the beginning of the film, two men on the boat reach out and one grabs her hand. In the next shot, she is too far below for them to reach her. Next, when Lara is climbing up the boat ladder, she steps up to the top and stands up fully. In the next shot, she is further down and stepping up again.
When they put their Wing-suits on, the arms and legs are not webbed. When they run and jump off the building they are not webbed, but when they start to glide they are. Also when they start to walk to the boat after they have landed, no webbing is visible between their legs.
When Lara is fighting the guy where all the terracotta warriors are, she throws two sticks at him pinning him to a large crate. The crate can not be seen at all while they are running through the warriors. The crate appears in the background and gets closer with each scene. He isn't standing directly in front of it, until the sticks are thrown.
When Lara and Terry are sliding down the rope, Terry starts out firing to his left with his gun in his right hand, right arm stretched across his body, and holding the rope with his left hand. Farther down the slide, he is shooting to his left with his gun in his left hand, left arm outstretched, holding the rope with his right hand.
When Lara and Terry are sliding down the rope, Lara's hair is all over the place. The shot cuts to the men shooting down at them then back to Lara and Terry. Lara's ponytail is tied in several elastics. It cuts again to the men above and then back to Lara and her hair is all over again. This happens several times.
They are almost touching the water when parachuting off the skyscraper, but the next close-up scene shows them coming straight down onto the ship. When Lara and Terry land on the ship, their parachutes are supposed to come down after them. You can see the chutes in their hands from the next far shot, but it happens too quickly.
Possible spoiler, at 1:38:12 during the sequence in the cave formation of the cradle of life, Reiss shoots at Croft, and as she dodges, a Red LED light is visible in the lower right corner of the frame (probably the battery light indicator for one of the set strobes).
Near the start, the underwater bikes first enter the water (wet for wet scene).
Watch the front of the lead (grey) bike. Just before the nose reaches the edge of the frame, two bright fast-moving bubbles go past diagonally left to right. These can only have come from the film crew.
When Lara and Terry escape from Reiss's lab in (Hong Kong) Times Square in Causeway Bay they go up a lift, and suddenly they leap off a skyscraper in the middle of Central. Causeway Bay and Central are two different parts of Hong Kong and it is not possible to go up a lift in Causeway Bay and end up on the roof somewhere in Central.
The black car coming into the street during the action scene in Shanghai is a RHD with number plates from Hong Kong, even when Shanghai and the rest of China uses LHD vehicles. Even if the car managed to drive all the way up to Shanghai from Hong Kong (impossible in the short time frame), the vehicle would require an additional cross-border plate issued by the mainland.
Jonathan Reiss's private jet is shown landing in what appears to be Kai Tak Airport in Hong Kong, with the distinctive HK skyline in the background. Kai Tak Airport was closed 6 July 1998 at 01:28, with the last arrival at Kai Tak occurring on 5 July 1998 at runway 13 at 23:38. As the film was released in 2003, Reiss should have arrived at the new Chek Lap Kok Airport on Lantau island - Hong Kong island's skyline cannot be seen from Chek Lap Kok Airport.
Logically assuming Lara left the London area in the C-130 aircraft she was seen parachuting from, the C-130 could not make the 5,592 miles at its cruising speed of 336 mph. It would take just over 17 hours.
When Lara shoots the computers in Reiss' lab, she only shoots the monitors. All this does is stop displaying what the computer is doing. Many say, that a knowledgeable woman like Lara should know to shoot the processor, not the monitor. However, later Reiss talks about keeping Lara alive as long as they know the computer finishes its translation; Lara only tried to delay Reiss, not to destroy the process (she couldn't do that anyways, since the computer boxes are not visible, and even if they are accessible to shoot, destroying the processors would take more time and effort than Lara had). We even see one monitor unharmed and showing the process bar.
When Lara is in the Luna temple getting the orb from the ceiling there are fingerprints on the base which holds the orb before she even touches anything around it. Also the finger prints are on the opposite side than where she rolls up to.
Lara and Terry appear to be sliding down the rope, when in fact they are being lowered down. The ropes do not move. There is a second pair of ropes anchored to the ground, but they are not moving either, as they are anchored to a couple of boxes.
The goof items below may give away important plot points.
During the fight scene between Reiss and Croft near the end, there is a sequence in which Reiss shoots Croft in the arm. She merely grunts as if this were nothing, but the next move executed by Reiss is to pull her hair, and she screams out loud. There is no way pulled hair hurts worse than a gunshot wound.