When Bambi sees the possums hanging upside down from a tree, they are oriented such that the shortest is hanging on the left and the longest is on the right. Bambi rotates his head to look at them. Doing this, the longest should now be on the "left". But in the film, the longest is still on the right.
When Bambi looks in the pond while in the meadow and sees Faline's reflection, he repeatedly looks at both his and her reflections. After Faline giggles, Bambi stops in awe and blinks twice. On the second blink, the reflection's eyes do not blink with Bambi's eyes.
When the dogs are hunting Faline through the forest, a brown dog is in front. In the close-up, the dog is right behind Faline, trying to bite her, but it is now turned grey. In the next shot, the dog is turned brown again.
When Thumper is laughing at Bambi just after we meet Flower, he rolls on his back and his normally white tail is brown. When he rolls back onto his belly his tail is white again. This appears to have been corrected for the 2005 DVD release.
Also during the fire sequence Faline awakes with brown eyes, instead of her usual blue, they remain brown all through the dogs/fire sequence and return to blue when she is at the thicket with her new babies.