1. Minimization of the crime
A number of people bought Polanski's spin that the crime involved a slightly-underaged woman involved in consensual sex. If you read the court testimony it's clear that's not what is at issue, but the purposeful rape of a 13-year-old girl.
2. That the victim doesn't want Polanski prosecuted
It's important to understand that crimes of this nature are prosecuted as "the People of the State of California versus" rather than as an individual versus the accused. It's not that uncommon for a victim to decide prosecution shouldn't be pursued -- but it isn't relevant, since the reason for the prosecution is to punish or prevent crime in the state. To be fair, anyone using this position should also have to precede it with "after receiving a huge financial settlement that hasn't been fully disclosed but is likely to be the most significant income in the victim's entire life, the victim doesn't think the case should be prosecuted."
3. That there's some "clear" problem with the case, the judge or the state
The appropriate action against any of these is to go to court. I understand that impression of mishandling of the case -- it's heavily fueled by the documentary, but now seems to be debunked at least to a degree -- and if it is true it can be settled in a court of law. Not by remaining a fugitive. When you are on the run from the law, you don't really get to nitpick the details of how your case was handled.
Since the first wave of interest in the Polanski apprehension, much has happened. He's now under house arrest at a luxury chalet. At least one petition-signer has realized she's on the wrong side of the case and changed her position. And there's been some movement in the courts which will likely resume after the holidays.
But the thing about being a celebrity is no one ever tells you you're wrong. So a director I otherwise respect is tut-tutting everyone for being so darn strict about rape, law, fleeing jail and other stuff that's just, you know, from a long time ago.
Terry Gilliam's Three-Reel Circus
MJ: Speaking of blowback, why'd you sign the petition supporting Roman Polanski?One reason the public didn't strongly call for Polanski's extradition in 2003 was that very few understood the facts -- instead believing the case to be similar to that of a rock star who is "shocked" to discover a groupie was only 17 1/2. In part, that's because Polanski's memoirs imply that, and because his lawyers and others have tried to popularize that view in opposition to the facts.
TG: I think the whole thing is so far in the past. Roman isn't a difficult fugitive. He could have been picked up any time. When he won the  Oscar for The Pianist, I don't remember the public demanding his extradition—because it didn't happen! The way people are behaving now, I don't even think they know the difference between extradition and execution. Here is a 76-year-old guy. The girl involved, everyone involved, has said, Forgive, forget, it's over and done with—until suddenly the long arm of the law decides now is the time to strike. His behavior was not right, but I think what is going on is even more suspect.
MJ: Hmm. Okay.
There's nothing suspect in being anti-rape or opposing someone who is able to flee and avoid punishment because they are wealthy. There is something suspect in those who use weasel-words like "his behavior was not right" in place of "raped a 13-year-old girl."
Facts matter, words matter.