Spectroscopy and the current state of our ability to determine the composition of extra-solar planets I was interested in learning more about the status of our scientific understanding and technological instruments regarding extra solar spectroscopy.
I am motivated by this almost 3 year old question/answer here at physics SE.
Specifically:

The composition of extra solar planet should be taken with a pinch of salt, the science is very new and uses instruments not designed for the task. Keep an eye out for new missions such as ECHO which might fly in the next 5 to 10 years...

Since it has been almost 3 years, can someone give an update on our current understanding on this subject? I am curious as to how accurate our measurements of the composition of  planets and stars outside our solar system are. Also, what is the impact of our atmosphere? Are we able to tease out the effects of absorption by our own atmosphere in order to get a clean signal?
 A: 
can someone give an update on our current understanding on this subject? I am curious as to how accurate our measurements of the composition of planets and stars outside our solar system are.

The most recent review article on this subject may be Exoplanetary Atmospheres (Feb. 2014). It explains "atmospheric observations have been reported for more than
fifty transiting exoplanets and five directly imaged exoplanets to date".  Sodium and potasium have been detected though visible spectroscopy.  Water, carbon monoxide, carbon dioxide and ammonia are studied via infra-red spectroscopy.
Another review article, Spectroscopy of planetary atmospheres in our Galaxy
 (2013), is slightly older but has more data and gives a better sense of signal to noise ratios.  

Also, what is the impact of our atmosphere? Are we able to tease out the effects of absorption by our own atmosphere in order to get a clean signal?

Many of the observations are made from space telescopes.  Some infrared wavelengths cannot be observed from the ground.  For planets observed by the transit technique, one takes the difference between the star's spectrum during and not during transit, so any signal coming from Earth should would be canceled out to the extent that it is constant over the time period of observation.  
