Oh dear, I must be archaic, stuffy, and very English English! I use 'should've thought' all the time! The others have answered the question. I'll just add a personal thought or two.... I use it sometimes as your dictionary says... to jokingly say that I think it is obvious... but I often use it as a rather sarcastic criticism: "I should've thought it was obvious if you stuck your fingers in the electricity socket you would get electrocuted." This would be said to someone who had just tried it... and was now suffering the consequences. I think I would sound rather unsympathetic!

I think Richard S from the USA has a nice example... look at his example number 3. "anyone with half a brain..." That's exactly what I'm thinking when I say it.

The sentence is subjunctive mood. Why express it in this way? I suppose it sounds more polite than to say, "I thought it was obvious."

My impression is that "I should have thought..." is somewhat archaic and stuffy. I think of it as a British expression that is not much used in the U.S. I agree with Philip that "I would have thought..." is more commonly used today. Although Randy is right that "I should have thought it was obvious." is more polite than bluntly saying "I thought it was obvious", the real issue is that "I should have thought..." and "I would have thought..." suggests the smallest possibility of being wrong (although the speaker probably feels he is right). It is a kind of British understatement that says "it was obvious; at least, I thought it was obvious until you proved that it wasn't obvious to you". This statement is somewhat insulting. Here are some more examples of using the phrase to form insults... Examples: 1) "I should have thought that 1000 Euros would last you all week." The speaker means that it didn't last you all week but he thinks it should have been enough (if you spent your money wisely). [NB: It's possible that the speaker is not being critical but expressing surprise that things were so expensive that 1000 Euros was not enough.] 2) "I should have thought you would check his references before hiring him." The speaker means that you didn't check his references first but he thinks you should have done so (and maybe you are now suffering the consequences of not having done so). 3) "I should have thought it was obvious." The speaker means that it apparently wasn't obvious to you but he thinks it should have been obvious to anyone with half a brain (which you apparently do not have).

On re-reading the original question, I realize that I didn't actually answer the specific question. 'Why isn't it working?' 'I should have thought it was obvious.' Example: Why isn't the electric fan working? I should have thought it was obvious (that it wouldn't work in a taxi where there is no electrical outlet to plug the fan into). That's an extreme example but it should give you an idea of what the phrase means.