[MrConfettiMan]

Unless I'm confused, when they're up in the mountains, Sam the pony isn't with them. When they're entering Moria, he reappears.

No, you're not confused. I noticed this, too, and it bugged me. The pony, I'm pretty sure his name was Bill :), was something I'd hope they might expand upon in the extended DVD but they didn't. (IIRC, they never introduced the pony until the scene outside Moria, right?) I wonder if they might show Sam "finding" him when he returns to the Shire in ROTK like he did in the books. Either way, though I doubt the casual observer thought much of it, those who know the books well most likely caught the problem with the scene(s).

[Restorer]

Ackk. You're quite right. The pony's name was Bill.

[Vast Buffalo Wing Conspiracy]

Listen to the commentary on the extended DVD. They talk about Bill the Pony. Yes, he is in every scene, including on the mountain, but he isn't always very visible. Some scenes, he is a two-person "pantomime pony" so obviously they chose not to make Bill very visible.