To me, if a boss is giving a new hire tasks where mistakes are highly damaging, then that is not a good boss. There's a reason more experienced people get paid more, and if they're not doing the hard/risky jobs then your boss isn't getting his money's worth!
I guess I'm at the point in my career now where I'm a senior engineer, and I can tell you that when thinking about which of the junior engineers to ask to do something, I don't think of the mistakes that they've made. I think of the improvements that they've made, their ability to understand things (this is a big difference from KNOWING things), and their willingness to learn. We have one junior guy who is more than happy to sit behind his desk and watch Hulu or Netflix all day if nobody is giving him anything to do. The other engineer in his office is busy reading ASME Y14.100 Engineering Drawing Practices. Who do you think I go to when I want someone to review my drawings?