We'll start with the primary jobs for which quotation marks are excellent:

The obvious one is when presenting an exact quotation --
"To be or not to be," is one of the most famous lines ever written.

When a quote falls within a quote, single marks are used for the inner statement --
He told her, "be careful, or I might have to go all, 'Frankly, my dear, I don't give a damn!'"

In this context, quotation marks are used in writing dialogue.


The trouble with quotation marks, as in the photographs here, comes with their use to indicate euphemism, irony or sarcasm.  Instead of quotation marks, one could use words like "supposedly" or "so-called" -- as in,
                                                            She was "feeling ill" and left early 
                                                                                      versus
                                                    She was supposedly feeling ill, and left early

You can appreciate the similarity, while the first one is probably a more effective statement of the dubiousness with which the speaker/writer views the claim of illness.

Which brings us back to the problem at hand. We frequently encounter the clear error of using quotation marks to indicate emphasis -- often with slightly comedic (or disconcerting) results. We're not quite certain how this situation has grown to epidemic proportions, but it has. 

To emphasize a word or statement (often a rule, regulation or command), one has quite a few tools in the typographical arsenal: italics, boldface, underlining, ALL CAPITALS or ANY COMBINATION of the foregoing. So, there is no shortage of options. Re-purposing of quotation marks to create another one is not only wrong, it's unnecessary.

Though the intended meaning in a statement containing errant quotation marks is understood, the essence result suggests the opposite.

We have encountered this twice in recent weeks -- either a straight-up error, or the result of auto-correct undermining the writer's meaning: the acronym AIDS rendered as "Aids."

One instance was in looking over a fundraising piece, the other when reviewing a medical information form from a dentist's office. All of the healthcare fields, and a few of the charitable/non-profit ones, need to be on the lookout for this specific error.

Auto-correct saves us from a lot of mistakes...but opens up whole new possibilities for embarrassment. If there are acronyms that you use regularly in your line of work, make a Ctrl+F review of them part of your standard editing/revision process, in order to ensure that they are all properly capitalized.

When abbreviating a multi-word name, the capitals are retained, partly as a clue that the resulting "word" stands for something else. "AIDS" represents the the term "Acquired Immune Deficiency Syndrome." Hence, must always be given in caps.


Bonus: 
Both "HIV," the Human Immunodeficiency Virus (that causes AIDS) and "AIDS" are abbreviations. However, AIDS is also an acronym, as the abbreviation creates a name that is read as a word. The alternative would be to refer to AIDS by its individual letters, as the disease ay-eye-dee-ess.

Whether or not an abbreviation is used as an acronym is not always obvious. The initial letters of the World Health Organization (WHO) creates a readable word, but the agency does not go by "the WHO (hoo)," as it could create confusion with the band of the same name. Ergo, even though it could be an acronym, it isn't used as such.

So, CIA (Central Intelligence Agency), IRS (Internal Revenue Service), BBC (British Broadcasting Corporation) and IRA (Irish Republican Army) are abbreviations. NASA (National Aeronautics and Space Administration), NATO (North Atlantic Treaty Organization) and IRA (Individual Retirement Account) are abbreviations that are also acronyms.

For vastly more on this topic, visit Wikipedia.