I like Phaze's answer as well.
However, as far as the
software goes, of course you can correct these situations, in several ways.
First, if you've busted a player out with the incorrect hitman, you can correct this in 2 ways, one of which is better than the other. First, you can always UNDO the bust-out, then bust the player out again, choosing the correct hitman. This is usually fine if you've discovered your mistake immediately after the fact. However, it has consequences if other players have since busted out of the tournament (ie, rankings won't be correct). The second way to fix this is to simply go to the Players tab, and edit the busted-out player. On the Edit Player Dialog, in the Tournament History section, you should see the player's bust-out. Edit that action and you can select the correct hitman there.
As for players who fail to let you know that they've busted out, probably the best (maybe the only) way to fix this is to simply bust them out when they tell you. Then go to the Players tab and press the "Adjust Rankings" button. Here you can adjust the
time that the player busted out, thereby fixing the rankings.
Note that depending on when the player informs you of their bust-out, you may not be able to select the correct hitman when you then bust that player out (their hitman may have since also busted-out). That's OK, just don't select a hitman. Then adjust the rankings, as described immediately above. After that, edit the player as described at the top of this post. Now that the player's "bust-out" is set to the correct time, the list of players from which you can choose a hitman will have changed to fit that time in the tournament, and you should be able to select the correct hitman.
Might be a bit painful, and might give more incentive to implement Phaze's answer.