How accurate are climate proxies in giving us a clear picture of global average temperatures throughout Earth history?
Overall, any individual proxy is not a reliable indicator.  It's the combination of multiple proxies that provides a clearer picture. 

For example, tree ring growth has been correlated with temperatures.  However, it's not without it's anomalies:


  ...from the middle of the 20th century tree ring growth was less than might have been expected from the temperature record... ([source]


(http://www.climatedata.info/Proxy/Proxy/treerings_introduction.html)) 

If we were to only look at tree-rings, we could not possibly trust on them as a reliable source, since they have known problems.

We can also use coral as a indicator of past climate.  However, it's also somewhat questionable:


  However, long (multi-centure) records are rare, and the possible influence of non-climatic influences has not yet been confidently established.
  source


Ice-cores are not immune to skepticism:


  An indisputable interpretation of ice-core oxygen isotopes in terms of
  atmospheric temperature variability, moreover, remains elusive, and
  precise annual dating can be difficult.


However, if we can combine these three indicates along with other indicators (pollen, earth bores, etc), we can increase the reliability of our understanding.  For example, if most indicators show a cold year, we can more reliability say it was a cold year.  

Combining these proxies together helps us to gain a clearer picture of the past environment.

Overall Reliability

However, with that said, the amount of uncertainty with the multi-proxy method is not small.

At the Workshop on Mathematics in the Geosciences, Blake McShane presented a new algorithm for estimating paleoclimate.  This algorithm provided a more reliable estimate by increasing the uncertainty of the predictions.  That's an important point that I will restate:

Through his talk, he showed that his method was more reliable because it was less certain.

Even that wide uncertainty level, he questioned:


  Indeed, this should make us increase our level of uncertainty (indeed perhaps 
  our wide intervals are in fact optimistically too narrow)!
  
  source


In the end, we can look at proxies for guidelines and trends, but they cannot be used for reliable readings.