I am not a database expert and have no formal computer science background, so bear with me. I want to know the kinds of real world negative things that can happen
A good explanation is contained in "Starbucks Does Not Use Two Phase Commit".
It's not about NoSQL databases, but it does illustrate the point that sometimes you can afford to lose a transaction or have your database in an inconsistent state temporarily.
I wouldn't consider it to be something that needs to be "fixed". The fix is to use an ACID-compliant relational database. You choose a NoSQL alternative when its behavior meets your application requirements.