Getting oxygen into the mix during fermentation can allow the botulism bacteria to grow. This is a particularly virulent bacteria, often fatal. I don't know if it has a characteristic taste (suspect not), but apparently it does show as a discoloured layer on top.
Having said that, I have made sauerkraut that did have an air breach early on and I ate it without ill effect.
Some tips from a website
Weigh it down: Keep your cabbage or other food down under the brine. If it floats to the top, it’s exposed to air, where it can pick up nasty bugs.
Brine it up: If you have too low a water/brine level, it gives undesirable bacteria and yeasts the food they need to grow on the surface. You can scrape off this “scum,” but you’ll be less likely to see it if you have a sufficient level of brine. Rule of thumb: one inch of brine above the sauerkraut.
Lighten the load: If you pack your jar too full, you may not leave enough space for the fermenting reaction to take place without causing an overflow. A good rule of thumb—pack your jars only 75 percent full. Less than that can leave in too much oxygen. More can push out your brine.
Salt it: Keep your salt ratio to three tablespoons to each quart of water. Salt makes the mixture less friendly to bugs.
Seal it: If your jar doesn’t keep out the oxygen, your yeast in the ferment could be oxidized, forming vinegar. It will also increase risk of mold. This may be the most important step in making fermented foods—make sure the environment is oxygen-free. If you notice browned cabbage, a yeasty odor, slime, or mold, could be your jars aren’t airtight. Jars with airlocks are recommended, as they keep out oxygen, but allow for off-gassing.
Measure it: Temperature is important in the making of fermented foods.