Learn English – Is “Here’s wishing xxxx” proper

It often implies that you have made a serious mistake, but more strictly it indicates that something you have done (or some turn of events) has left you looking embarrassed or foolish:

Murray knows all about the Chilean 12th seed — he practised with him last week — and the British number one realises he could be left with egg on his face if he leaves Gonzalez an easy, mid-court ball.

Where it came from (source):

I know of two suggestions for where it came from. The late John Ciardi suggested an origin in the lower-class and more rowdy kind of theatrical performance, in which an incompetent actor would have been pelted with eggs and forced off the stage. The other is that it was a comment on a minor social gaffe at a meal, when poor manners or sloppy eating left egg around your mouth.

And also (source):

From the embarrassment suffered if the yellow yolk is on ones lips or beard after eating a soft boiled egg in one of those egg cups, a favorite breakfast of the upper crust... Yellow egg shows up especially well on a beard or mustache.

You catch more flies with honey than vinegar or, sometimes you catch more flies with honey is an English proverb. It doesn't have a counter-intuitive meaning--if you are trying to catch flies, you are literally going to attract more with honey. That is, you're going to get what you want (in the proverb flies, but in life any goal) with sweetness rather than acidity.

This answer explains it similarly:

Flies represents anything you want to achieve. Honey (sweet) represents anything pleasant that you do to get what you want. Vinegar (sour) represents anything unpleasant that you do to get what you want. It tells you to use nice methods rather than unkind methods in dealing with other people.

This is a saying that means: you will be more successful in life being sweeter, or nice rather than being, mean to people, not nice and doing hurtful, dishonest things in life.

This forum makes some guesses at its origins, noting:

The proverb has been traced back to G. Torriano's 'Common Place of Italian Proverbs' . It first appeared in the United States in Benjamin Franklin's 'Poor Richard's Almanac' in 1744, and is found in varying forms..." From "Random House Dictionary of Popular Proverbs and Sayings" by Gregory Y. Titelman (Random House, New York, 1996).