the phrase "so-called" - is it positive or neutral?

Depends on the exact context.  But I think it would be almost always negative.

A so-called expert ...
Our so called president ...

I can't think of a positive example, but I will keep trying.

The phrase suggests that the speaker does not agree with the associated title or description.

More of a reverse than an actual positive:
"The so-called 'waster' who founded this internationally recognised successful company"

Someone who was once, probably famously, known as not useful who can now be justifiably proud of their achievements.

It's usually meant as a negative though. As said earlier, where the speaker doesn't accept that the title is deserved.

Not always negative and not always a reverse of an actual positive; although that is probably the most common usage. But, positive? I don't think so.

"So-called" is sometimes used when describing a previously unnamed entity, and someone gives it a new or temporary name, and when others then reference that name, they might preface it with "so-called", so as to indicate that the name referred to is fairly new and/or not having official status. Eventually, if the name becomes solidly part of the language, then the "so-called" preface could be sometimes be dropped - is my guess.

The so-called definition of "so-called" has different meanings depending upon whether you are British, or American (USA, to be specific).

American

• named or called in a particular way: Married taxpayers are hit hard by the so-called marriage penalty.

• People or things that are so-called may not fit their name: These so-called experts don’t know anything.

The first definition is just giving a preface of so-called before marriage penalty, because in tax laws, marriage penalty is definitely not written into the tax code in those terms. In this case, there is no reversal, and although the usage is often spoken of negatively especially by married people, but perhaps positively by single people who don't plan on marriage for awhile, there is no indication that the expression "marriage penalty" is being refuted as an inappropriate term. In this case, the term fits the tax code.

British

• used to show that you think a word that is used to describe someone or something is not suitable or not correct: It was one of his so-called friends who supplied him with the drugs that killed him.

• used to introduce a new word or phrase that is not yet known by many people: It isn't yet clear how dangerous these so-called "super-rats" are.

http://dictionary.cambridge.org/us/dictionary/english/so-called

Another example of explaining that a so-called name is just a shorthand unofficial name for an official entity:

The Constitution grants the president 10 days to review a measure passed by the Congress. If the president has not signed the bill after 10 days, it becomes law without his signature. However, if Congress adjourns during the 10-day period, the bill does not become law.

How do people refer to this succinctly? They refer to this as the so-called pocket veto.
Someone invented that expression, and others used it.

>> inaccurate or questionable applied to the noun
I guess I am the only one who disagrees that this is the only definition of so-called. I agree that "inaccurate or questionable applied to the noun" is the prevalent usage of so-called; but as I posted before, there is another definition which is not negative at all and also does not convey inaccuracy (but nor is it positive).

>> god particle

excellent example. This term was created to popularize science for the purpose of getting grant money to further their explorations, in my opinion.

So-called used here is not meant to be negative nor is it meant to say that God particle is inaccurate. For it to be inaccurate one would have to know what a God Particle is and then too suggest or imply that it is not a God Particle. But God Particle is just a made-up term, that is used to give a name to some very complex theory for the masses, in my opinion.

thanks all for the context ...in which can be used and example. truly appreciate