In attempting to answer this question, the first type of observational error that Hegerl et al. investigate is sampling error.  Their analysis of this subject takes into account, in their words, "the changing density of available data through time for each grid box," that is, for each 5° latitude x 5° longitude parcel of the earth's surface; and it estimates "the effect of missing grid boxes on large-scale averages."  The bulk of their paper, in fact, is almost totally devoted to this one type of error; and, as might be expected, they conclude from their analysis that its effect is "small."

The second type of observational error considered by Hegerl et al. is instrumental error.  In this category they identify two subtypes: random error and systematic error.  In considering the first of these subtypes of instrumental error, they conclude that its effect is even less significant than that of sampling error, calling it "very small."  But when they get to the second of the subtypes, they conclude that its effect "cannot be assessed at present."

Cannot be assessed at present.  Think about the implications of those words.  If we cannot assess the magnitude of this particular type of error, or even estimate it (as the authors say in another place in their paper), what good are the temperature trends that are derived from the data to which the unknown error or errors apply?  Not knowing how big or how small they might be, logic requires we acknowledge the simple truth that the temperature trends produced by these data are, for all practical purposes, meaningless.

So what are the types of things that fall into this intriguing category of unassessable systematic instrumental errors?  Over the world's oceans, Hegerl et al. mention "errors in the corrections for the transition from bucket to ship intake measurements."  Over land, they cite "urban warming of stations."  And potentially applicable everywhere are "changes in the time of day measurements were taken."

What do the authors do about these potential errors of unknown magnitude?  In a word: nothing.  They note, for example, that "no corrections have been applied to sea surface temperatures after World War II," suggesting that any needed corrections "are estimated [our italics] to be small [our italics]."  They also note "it has been estimated [our italics] that temperature trends over rural stations only are very similar to trends using all station data, suggesting that the effect of urbanization on estimates of global-scale signals should be small [our italics]."  And they make these remarkable self-serving estimates after having just written that "it is very difficult to estimate the magnitude of those errors."

Isn't it interesting that while admitting these particular errors are either very difficult to estimate or cannot be estimated at all, Hegerl et al. proceed to readily make just such estimates?  Even more interesting is the fact that the error estimates they make are all "small."  Since logic would not lead one to such a conclusion (for how can any estimate be made of something that "cannot be estimated"), and since real-world data would not lead to such a conclusion (see, for example, Urban Heat Island in our Subject Index), we can only speculate about what would cause the authors to come to such a politically-correct conclusion.  And so can you.  In fact, we encourage it.

But what about datasets other than the one of Jones et al.?  Might there not be a better one that could be used to make the case for CO2-induced global warming?  Probably not.  In the words of the authors, "although several datasets exist for the most recent surface air temperature observations [i.e., the ones that show "unprecedented" global warming], these are mostly based on the same observations."  Hence, if the Jones et al. dataset can't do the job, neither can any other such dataset of global dimensions.

So where does all this leave us?  Sadly to say, with very little into which we can truly sink our teeth.  To be brutally honest, in fact, several of the systematic instrumental errors associated with essentially all global datasets of near-surface air temperature are of unknown magnitude, which means that any temperature trend derived from those data is highly questionable and should be taken with a grain of salt.  Unfortunately, that grain of salt is highly prized by the functionaries of the Intergovernmental Panel on Climate Change and their band of political cheerleaders.  Though it may cause them to salivate in anticipation, when the time finally comes that it is thrust down the throats of the rest of us, we will all surely gag on it.

References
Hegerl, G.C., Jones, P.D. and Barnett, T.P.  2001.  Effect of observational sampling error on the detection of anthropogenic climate change.  Journal of Climate 14: 198-207.

Jones, P.D., New, M., Parker, D.E., Martin, S. and Rigor, I.G.  1999.  Surface air temperature and its changes over the past 150 years.  Reviews of Geophysics 37: 173-199.