Is there such a thing as a wrong opinion?
It depends upon the level of objectivity involved.
1. If an opinion is strictly of an objective measure, then it may be proven wrong. E.g. an opinion that Moon is 100 miles afar. This is an incorrect assumption that can be proven wrong.
2. If an opinion is mostly subjective, however is dependent upon a few objective qualifiers such as experience or exposure, then it may be put on a scale of "more informed" to "less informed". E.g. a movie critic proving an opinion for a film. Clearly he has had more exposure to cinema and therefore his opinion may hold slightly more weight than someone who has never seen a movie before, and therefore would like any sense of novelty.
3. If an opinion is entirely subjective, i.e. there are no second or third persons being affected by your assertions, then it cannot be wrong or more or less informed. E.g. blue is a soothing colour. This is an entirely subjective assertion.
So, I suppose, opinions -- as far as they are subjective and claim to be subjective -- cannot technically be wrong.
If not then does that mean that pedophiles and serial killers have an equal opinion to your own?
Yes.
It's important to make a distinction here between having an opinion, and acting on an opinion. The former does not matter because it is self-contained, and therefore, of equal value to any self-contained opinions I might have. It only matters if said opinion is acted upon, and thus quantified.
If so, then by what process do you determine what opinions are correct and which are wrong?
N/A, see first answer.
Do all opinions deserve equal respect? Do the opinions of pedophiles and serial killers deserve just as much respect as your own?
I'll use examples.
If their opinion is that my 3-year-old daughter is sexy, then I will respect that as long as they do not touch my daughter or come near her, and I will go through lengths to ensure her safety.
If their opinion is that my 3-year-old daughter is their daughter, but it's fine if I raise her, then I will point out that this is wrong because I saw her being born and I have more experience to conclude that she is my daughter.
If their opinion is that my 3-year-old daughter is actually 16, then I can say lol ur wrong.
Should opinions be only based on personal experience? If I was raised by a bunch of sociopaths to be a sociopath then would you consider the opinions I have based on that experience to be as valid as your own?
Yes/no, too vague to answer.