Factual error: When the Titanic sinks all six dwarves and Kevin end up in the sea clutching a lifebelt. The water in which the Titanic sank was freezing - that is how most of the casualties died, by freezing, not drowning. In water like that you'd be lucky to stay conscious for more than a few minutes. Despite this none of them show the slightest effect of the cold. Maybe the dwarves have some 'magical' ability to withstand lethal cold, but Kevin doesn't even react to being plunged into freezing cold water. He'd be screaming in pain, but he doesn't even show the slightest sign of discomfort.
Revealing mistake: At the beginning when the ruler is making his speech, you can see his modern day fillings in his upper molars.
Continuity mistake: Chief is tied to his kennel around the collar. But when Copper cuddles up to him for the first time, the rope tied to his collar disappears for a shot. (00:10:35)
Continuity mistake: At the end of the film the plane they are initially flying on is a typical passenger plane, but when the Muppets are thrown out, the plane is one used for skydiving.
Continuity mistake: When Yosemite Sam tells the devil that he has "the very varmint in mind", you can see there are no flames coming up from the pit behind him, but in the next shot flames have suddenly appeared.