The film industry is small and very interconnected. Word travels fast.
Personally, from my point of view in my own line of work (i.e. on set in camera department) it would often depend on a crew member's level of experience, how much I liked him/her and what the 'offense' was.
For example, dropping a lens, or breaking a camera is a great way to get a break from work for a few years.
If you're inexperienced, sometimes I'll understand, though I probably won't work with you again until you've gained some experience.
If you're experienced, it comes down to whether you're experienced and incompetent, or just made a mistake. We all make mistakes from time to time, and some mistakes are worse than others. If you're experienced but generally incompetent, you'll find yourself getting less and less work. If you're experienced and just make a mistake, it will depend on how drastic that mistake was.
Keep in mind that it's not just your technical knowledge and skill on set, it's also the way you present yourself and perform. If you spend too much time talking on set, not enough time working properly, don't act professionally, are consistently late, or even sometimes if you're just a difficult person to work with, you'll find yourself getting less and less work.