How is the specificity and sensitivity of a "gold standard" measured? I know when a new measurement technique is developed, it's sensitivity and specificity is measured against a "gold standard."
I'm wondering what the gold standard itself is measured against?  How was its specificity and sensitivity determined?  How does one decide to replace one "gold standard" with another that might have higher specificity and sensitivity?
 A: My expertise is in DNA genomics, so I'll use it.
Creating a gold standard reference is critical in genome sequencing. While comparing an experiment to a gold standard is simple, creating the gold standard itself is a very difficult job. My institution has a team of world-class scientists for just doing that. They would use domain knowledge (e.g biology and bioinformatics) to verify the reference. It's a highly technical process, and has nothing to do with statistics.
The gold standard reference is considered a set of perfect true-positives. There is no need to calculate sensitivity and specificity. Everything is measured relative to the standard. If you want to change the standard, you'd have to convince the scientists, and it's not so easy.
A: The gold standard is suppose to be the true - by definition its specificity and sensitivity should be prefect.
In many cases, is easy to create a gold standard in such a level. For example, there are cases in which finding the correct label is hard at a given point of time but easy after a certain period as in loan return and customer churn.
Other cases are when it is easy to judge each case but hard to define a rule (a classifier) like in judging if there is a cat in a picture.
Not that in some cases the definition itself can be vague and the gold standard can be used to enforce interpretation (e.g., is a lion considered a cat? and a leopard?)
There are cases in which building a gold standard that is totally reliable is hard. It is common when using crowd sourcing for labelling. 
The first good news that you can aggregate the labels while considering the precision and recall of each labeler using a Dawid-Skene estimator Maximum likelihood estimation of observer error-rates using the EM algorithm (1979)
The other good news are that you can learn in the presence of white noise (Learning from noisy examples) and to some degree even with malicious errors (Learning in the presence of malicious errors) so even if your gold standard is not perfect you might still be able to learn well.
A: 
I know when a new measurement technique is developed, it's sensitivity and specificity is measured against a "gold standard

No, not quite/not necessarily.  I think you and I have a different definition of gold standard, so we're framing the matter a little differently from one another.  It doesn't really matter, as the two positions will be reconciled by the end of the answer.
The Cliff's Notes:
The sensitivity and specificity of a measure is calculated by comparing it against the "true state of affairs". If this is unknowable or too onerous for widespread use, then there will be an equivalent operational definition that one works with.
Take, for example, measurements of time (they too can be converted to sensitivity/specificity). The definition of 1 second is the distance travelled by light in a vacuum in 1/299792458 second. 
I presume that you view this as the gold standard measure of time, whereas I would define it as the objective standard of time. Instead, I frame the gold standard of time as an atomic clock.

I'm wondering what the gold standard itself is measured against? How was its specificity and sensitivity determined? How does one decide to replace one "gold standard" with another that might have higher specificity and sensitivity?

The above example of time is useful in getting your head this issue. 
It's just not possible for an atomic clock to be more precise than the working definition of time itself.
That said, under some circumstances, what you're saying makes far more sense, both conceptually and intuitively. This is particularly a relevant if there is no objective marker to speak of, per se.
A good example of this problem is with psychiatric disorders. A questionnaire that measures, say social anxiety disorder may have a sensitivity and specificity of 0.75 and 0.80, but this is problematic when its predictive utility is based upon the "objective" diagnostic standard of a clinical interview… which itself is susceptible to lack of interrater reliability. In some sense what you're measuring is the shadow of a shadow.

How does one decide to replace one "gold standard" with another that might have higher specificity and sensitivity?

In your definition of gold standard measures, think of the gold standard as being a representation of an objective measure. Here, the gold standard cannot be replaced without obliging us to redefine what it is that is being measured in the first place.
