Were the sentences in the following well-publicized cases appropriate in achieving the goals of the criminal justice system?
Pete Rose- Tax Evasion
Joseph Hazelwood- Captain Exxon Valdez
Daniel Rostenkowski- Mail Fraud
That depends on what you believe the goals of the criminal justice system are. If we can agree, in general, that those goals are to convict criminals and sentence them in a way that fits their crimes, then these cases become problematic.
What these three particular cases have in common is that they all involve either celebrity, money or power, and in some cases all three. It is much less likely a person with one or more of those attributes gets convicted or given a lengthy sentence.
For Pete Rose, one could argue his crime was non-violent, he did have to serve five months in medium security prison and that such a sentence seems appropriate for a tax evasion charge, given that he paid the back taxes and fines and performed community service. So of the three cases, his seems to come closest in my mind to being "just".
Joseph Hazelwood, through extreme negligence of command, caused billions of dollars in economic damage, but merely lost his Master's License for nine months and paid a fine, along with some community service. Given the economic dislocation the Exxon Valdez disaster caused and the lives it ruined, not to mention the long term environmental damage, his sentence seems quite disproportionate to the crime.
Daniel Rostenkowski, former Chair of the House Ways and Means Committee, represents an example of power and its influence over the justice system. His corruption was on a massive scale and was blatant in nature, yet his sentence was for 17 months in prison, of which he served 15. Later, and no doubt, owing to his position in and history with the Democratic Party, he was given a full pardon, something the vast majority of people who commit such large scale white collar crimes never receive.
Keep in mind that any answer to this question has to be subjective in nature.