It’s “cut the muster,” not “cut the mustard.”

This etymology seems plausible at first. Its proponents often trace it to the American Civil War. We do have the analogous expression “to pass muster,” which probably first suggested this alternative; but although the origins of “cut the mustard” are somewhat obscure, the latter is definitely the form used in all sorts of writing throughout the twentieth century. Common sense would suggest that a person cutting a muster is not someone being selected as fit, but someone eliminating the unfit. See the alt.usage.english faq explanation of this term.

It’s “carrot on a stick,” not “carrot or stick.”

Authoritative dictionaries agree, the original expression refers to offering to reward a stubborn mule or donkey with a carrot or threatening to beat it with a stick and not to a carrot being dangled from a stick. Further discussion. This and other popular etymologies fit under the heading aptly called by the English “too clever by half.”

“Spitting image” should be “spit and image.”

According to the Oxford English Dictionary, the earlier form was “spitten image,” which may indeed have evolved from “spit and image.” It’s a crude figure of speech: someone else is enough like you to have been spat out by you, made of the very stuff of your body. In the early 20th century the spelling and pronunciation gradually shifted to the less logical “spitting image,” which is now standard. It’s too late to go back. There is no historical basis for the claim sometimes made that the original expression was “spirit and image.”

“Lion’s share” means all of something, not the larger part of something.

Even though the original meaning of this phrase reflected the idea that the lion can take whatever he wants—typically all of the slaughtered game, leaving nothing for anyone else—in modern usage the meaning has shifted to “the largest share.” This makes great sense if you consider the way hyenas and vultures swarm over the leftovers from a typical lion’s kill.

“Connoisseur” should be spelled “connaisseur.”

When we borrowed this word from the French in the 18th century, it was spelled “connoisseur.” Is it our fault the French later decided to shift the spelling of many OI words to the more phonetically accurate AI? Of those Francophone purists who insist we should follow their example I say, let ’em eat bifteck.
See also Commonly Made Suggestions