When the Grinch gains his strength to prevent the sleigh from falling off Mt. Crumpet, he lifts the sleigh over his head. Max the dog is left on the snow at first (when the sleigh is first raised), but then jumps up to the runner a moment later.
When the Grinch puts the antler on Max's head it has five prongs. But when Max tips forward, one of the prongs disappears as it's hidden behind his body. The Grinch only cuts off four prongs, but when Max goes upright again, the fifth prong is still gone.
The "antlers" that the Grinch puts on Max's head at first has a branch on the back which is hidden behind his body when the weight of it causes the head to sink. After the Grinch saws off the extra branches and Max straightens up, the branch is no longer there, even though it was not sawed off.
In all the long shots of Whoville, we see two hills behind town, on which several trees are growing. During the first shot, right before the Whos sing "Welcome Christmas", both hills have a large number trees growing on them, but during the reprise, all but a few trees have disappeared.
At the end when the sled full of Christmas stuff is on the mountaintop, it starts sliding off the edge. It's going fast enough that it should be long gone by the time the Grinch reaches it, but when he does it's still right near the top of the mountain.
In the last scene of the Grinch carving Roast Beast, as he passes the plate to Cindy-Lou Who, and she hands the plate to Max the dog, the Grinch's eyes turn from blue to red (for a split second) and then return the blue.