The "Hockey Stick" controversy

A quasi-global instrumental temperature record exists from approximately 1850. However, to construct a millennial-scale record, proxies for temperature are required. Consequently, there are issues concerning the accuracy with which these proxies reflect actual temperature change, their geographical coverage, and the statistical methods used to combine them. [source]

... The hockey stick controversy has to a large extent been focused on Mann and on the MBH98 reconstruction on which he was the lead author. ...
... In 2003, Stephen McIntyre and Ross McKitrick published "Corrections to the Mann et al. (1998) Proxy Data Base and Northern Hemisphere Average Temperature Series" in the journal Energy and Environment 14(6) 751-772, raising concerns about their ability to reproduce the results of MBH. ...


The claim
"... a rapid warming during the 20th century that culminates in anomalous late 20th century warmth ... " [source and source]


Problems replicating the results:
The M&M Project: Replication Analysis of the Mann et al. Hockey Stick [source]
... If the flawed bristlecone pine series are removed, the hockey stick disappears regardless of how the PCs are calculated and regardless of how many are included. The hockey stick shape is not global, it is a local phenomenon associated with eccentric proxies. Mann discovered this long ago and never reported it. ... [source]


Below are the findings and conclusions of the 2 third-parties that were asked to asses the validity of the original claim: The Wegman Panel and the National Academy of Sciences.

Some findings [source]:
Findings
In general, we found MBH98 and MBH99 to be somewhat obscure and incomplete and the criticisms of MM03/05a/05b to be valid and compelling. We also comment that they were attempting to draw attention to the discrepancies in MBH98 and MBH99, and not to do paleoclimatic temperature reconstruction. Normally, one would try to select a calibration dataset that is representative of the entire dataset. The 1902-1995 data is not fully appropriate for calibration and leads to a misuse in principal component analysis. However, the reasons for setting 1902-1995 as the calibration point presented in the narrative of MBH98 sounds reasonable, and the error may be easily overlooked by someone not trained in statistical methodology. We note that there is no evidence that Dr. Mann or any of the other authors in paleoclimatology studies have had significant interactions with mainstream statisticians.

Moreover [source]:
... they found that the full amplitude of century-to-century variations were underestimated to an increasing degree as the noise level was increased. Thus, the reconstruction of century-long trends has substantial uncertainty when it is based on data that exhibit year-to-year variability.
...
Some of these criticisms are more relevant than others, but taken together, they are an important aspect of a more general finding of this committee, which is that uncertainties of the published reconstructions have been underestimated.

In conclusion
As a good friend of mine said a few days ago about this controversy, it is never a good idea to mix science and politics ;)