We all know the situation – someone gets really angry; starts shouting; and loses control. Giving the impression that they are ridiculous and helpless rather than self-possessed. You should therefore remember to stay calm and be polite but firm. Documented criticism, made quietly but clearly, will always be streets ahead of a tantrum.
What is, however, even more important is that private criticism should remain private. It is not something that should be shared with the rest of the world. Always be sure to conduct such conversations one on one. This will ensure that the other person will not be embarrassed but instead receive valuable feedback on how they could do things better in future. This applies to criticism from both the bottom up as well as from the top down. Your boss should also be self-assured enough to be able to deal with having possible errors pointed out to him or her. If this is not the case, then why not point this out – in private?