Please note that the following applies to English Common Law. Theoretical Common Law is different, but also tends to not exist.
Advantages of Common Law: Allows judges to create laws in a system that sometimes is too clogged up and corrupt to accomplish anything within a reasonable amount of time (The United States federal legislature is like this)
False. Common law judges do not create law, they merely interpret it. It all stems from legislature, but since legislature cannot be written for every specific instance for obvious reason, it is up to judges to decide how the law applies to each case.
Advantage of Common Law: Allows judges to change the laws if the law no longer reflects the accepted norms of society.
Also false. Judges cannot contradict statute law. If they did, it would simply be appealed and the decision overturned.
example: In 190X, a man from Boston was found to inherit $10,000 from his father's will. The man from Boston knew of his status in the will, and killed his father to get the money. Should he stand to inherit the money? Technically, yes. But the judges considered that to be silly to allow him to get the money, so the judges denied him his inheritance. Was what the judge did correct? If so, you agree with Common Law.
That more Natural Law vs. Moral Law than it is Common Law.
Disadvantage: It makes the law unpredictable at times. Which is why Common Law Judges, for the sake of predictability in the law, stick a lot of times to something called precedent.
You've got it backwards. Common law is predictable precisely because judges are required to follow precedent. Always. The only time they can come up with a new interpretation is when they can show the current case is markedly different from the previous cases providing precedent.
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Personally, I love the idea of common law. It makes administration vastly easier. Problems can arise when judges inevitably disagree on interpretation of the law, but that's why you have a small Supreme Court that will analyse the spirit of the law and apply it. As long the majority of people have faith in the Supreme Court of their country, common law tends to work.
And if things should ever fail, the government is free to step in and correct the situation. The second that legislatures step in and contradict precedent, the statute becomes the new ruling doctrine.