(at around 1h 12 mins) When Zira drowns and dies, the scar above Kovu's eye disappears, then reappears later.
(at around 8 mins) One of the bugs on Timon's platter changes color.
The number of lionesses in both prides change repeatedly.
(at around 1h 4 mins) When Kovu and Kiara are looking into the pond and their faces are connected half and half, Kovu's scar is on the wrong side in the reflection in the pond.
(at around 1h 14 mins) At the end of the film all the lions are sitting in a circle. When Simba, Nala, Kovu and Kiara leave the circle and walk along the middle, the lions are now sitting in a straight line.
When Rafiki is singing Upendi, he sings "It's a long way down off the Lover's Leap, but falling's half the fun".
Lover's Leap is actually when a heartbroken lover takes a leap to end their life.
(at around 30 mins) The topi (large brown antelope) that Kiara pursues make wildebeest noises.
Throughout the beginning of the movie, purring is heard. In real life, Lions really aren't able to purr.
(at around 41 mins) The species of birds that Timon and Pumbaa try to scare off is the dodo, which has already been extinct since the mid-1600's. Yet we see those birds flying when the 4 main protagonists (Timon, Pumbaa, Kiara, and Kovu) were trying to scare them.
Rafiki sings about beating the bush "from Tanganyika to Kilimanjaro". Tanganyika hasn't existed since 1964; modern-day Tanzania is where part of Tanganyika used to be.
When Kovu gets his facial scar, Zira's claws slashed Kovu's face right to left, yet the scar is vertical. This was likely intentional in order to show the parallels between Kovu and Scar, and how Zira wanted her son to be just like him and assist in taking down Simba.
(at around 1h 3 mins) When Kovu and Kiara reunite in "Love Will Find a Way," Kiara doesn't seem to notice the fact that Kovu now has a scar across his left eye. On the other hand, however, she might already know about his scar, but just doesn't care since she knows Kovu will never be evil, like Scar was. Plus, since, everyone in the Pride Lands saw the scar on his face, it's likely Kiara saw it as well but never saw him as evil as his mentor.
(at around 1h 12 mins) It might take some time to notice, but after Zira drowns one of Kiara's claws is not colored in.
When the movie was released in 2004, Kovu's scream towards the crocodiles was reanimated into two frames. The scream is heard but the actions don't match the screaming. It appears as if he's not screaming at all.
Okapis appear several times in the film. Whilst these animals are native to Africa, they live in dense rainforest, not on the plains where lions are found (and where they appear in the film). They would never naturally encounter lions.
Kiara teaches Kovu to roar in order to scare away the birds with Timon and Pumbaa. However, Kovu already knew how to roar, as when he first confronted Simba as an adult after saving Kiara's life, he answered Simba's roar with one of his own.
When Simba, Nala, Rafiki, and Zazu are seen arriving at the pond after Kovu saves Kiara from the fire Timon and Pumbaa are not with them and are not seen at Pride Rock when Simba, Nala, Kovu, Kiara, Zazu, Rafiki, and the lionesses return to Pride Rock for the night. It is most likely they took shelter somewhere from the fire and decided to stay there for the night since they were shown the next day trying to chase birds away from eating their bugs.
When Zira and Kiara fall off the cliff and Kovu screams for Kiara he screams Kiera instead of Kiara.