Specifically, the reason you whisk it in slowly at first is to create small drops. If you just dump the oil in fast, it will adhere to itself and make it impossible to break up into droplets dispersed in the vinegar (or other water based liquid, such as lemon juice). This is the definition of an emulsion: tiny droplets of one liquid evenly dispersed in another. Once you've got the emulsion started, you can pour in the oil a bit faster because the already suspended droplets reduce the room for a big blob of oil to form, and act sort of as "sandpaper" to break up the incoming stream as you whisk.
As a health inspector for over 20 years, I am astounded by the lack of awareness that food safety controls are based on science and not on individual inspectors' personal fears and bad moods. Botulism control is based on some of the following facts: botulinum spores are commonly found in soil and on vegetable surfaces, botulinum grows in low or no oxygen envt., botulism has high virulence. (Virulence is a technical term for the fact that a high number of botulism victims end up dead (like Listeriosus of raw milk fame), in contrast to other food borne illnesses like Staph or Campyllobacter.) When considering the fact that botulinum grows slowly, and food borne illnesses whack people more often with weak immune systems, such as the elderly, the ill, and the very young, the food producer may have just been lucky that the product never created a problem, or the very real option that a problem was never narrowed down to the product.
As to the argument that old time recipes have been made for centuries, as in this case, (I am a bit of a foodie and Italian), the big difference is that many products were never made for mass production and or to stick around on shelves for long periods of time, and if so, any data, let alone food safety data, is unavailable for historic food products. In fact, the link between bacteria and illness was scientifically proven by Koch as late as the late 1800's. Another fact is that the CDC's data shows that outbreaks over the last 50 years are fewer, involve much higher number of victims and are more often associated with mass production and distribution of food. My health dept. receives notices of food recalls at least once a week.
In the case of botulism and fresh garlic in oil, it's considered so risky that acidification is required nationwide. In California, there is a state lab that specializes in evaluating botulism safety for commercial operations. (It's funded by taxes to keep cost to businesses low and is considered a public service.) I would recommend that producers contact their State health depts. and work with them to identify any and all options available for the canning and sale of any low acid food - including acidification, using dried ingredients, temperature control, flash heating (called a "kill step"). The majority of us inspectors truly focus on how to sell food safely and do not approach their jobs as stopping people from making a living. And surprise surprise we don't always think alike, just don't get me started. However, I'll finish with the following consideration of the implication that "life has it's many risks" argument that we inspectors hear often. When it comes to death, the public, the politicians and the members of responsible industry itself does not tolerate "a little death."
Best Answer
In my experience, that is completely normal and will not harm its flavor at all. You just need to warm it up before serving so that you can re-mix / emulsify your sauce / dressing. It congeals in the fridge much like any other fat will (think butter or bacon grease). Apparently, extra virgin olive oil may suffer from condensation in the bottle affecting the flavor. It may also turn cloudy.
But in general, you should be fine. Even if it does go bad, it should just affect the flavor and not be harmful, just gross. So if it tastes bad, toss it. Otherwise you're fine. Note: I'm just talking about the oil going rancid, not anything else you might mix with it.