Wikipedia has this for an introduction on Spencer, “Roy Warren Spencer is a climatologist, Principal Research Scientist at the University of Alabama in Huntsville, and the U.S. Science Team leader for the Advanced Microwave Scanning Radiometer (AMSR-E) on NASA's Aqua satellite. He has served as Senior Scientist for Climate Studies at NASA's Marshall Space Flight Center. He is known for his satellite-based temperature monitoring work, for which he was awarded the American Meteorological Society's Special Award.”
His credentials are real. What he is also known for a series of papers he published in the early 1990s with another scientist, John Christy. In these papers they claimed their analysis of satellite temperature measurements showed no warming in the atmosphere. They became the heroes of the global warming denier crowd as a result.
But, by the end of the 1990s it was shown they were not only wrong, they were so wrong they even admitted it themselves, but only after being confronted with the evidence from others. Separate studies showed four significant flaws in their work. What I find really interesting is that these two are undeniable experts in this process, yet they made four major errors in their data and each of those errors worked to remove global warming. And, these errors were found by other people. I really have to wonder, what are the chances that two experts will make so many errors and all of those errors work to show the results they wanted? If they were random errors you would expect at least one of them to work to enhance the global warming evidence.
I will not say they deliberately falsified their research. I believe there is enough evidence to convince a jury, but it has never been put to one, so we will probably never know. But, there is certainly enough evidence to convince me.
Spencer, though, continued to do an end-around on peer-reviewed science and was able to get a paper published in a journal that had nothing to do with climate change (I will speak on this more below). This from DeSmogBlog:
In July 2011, a paper co-authored by Spencer was published in the journal Remote Sensing, “[which is] a fine [peer-reviewed] journal for geographers, but it does not deal with atmospheric and climate science,” RealClimate found. 
His paper looked at a potential connection between clouds and global warming. The paper received significant media attention, and climate change skeptics claimed that it “blow[s] a gaping hole in global warming alarmism.” 
Within three days of the publication of Spencer & Braswell's paper, two climate scientists (Kevin Trenberth & John Fasullo) repeated the analysis and showed that the IPCC models are in agreement with the observations, so refuting Spencer's claims.
In Andrew Dessler's view, “[This] paper is not really intended for other scientists, since they do not take Roy Spencer seriously anymore (he’s been wrong too many times). Rather, he’s writing his papers for Fox News, the editorial board of the Wall Street Journal, Congressional staffers, and the blogs. These are his audience and the people for whom this research is actually useful — in stopping policies to reduce GHG emissions — which is what Roy wants.” 
In response to the flawed peer review that allowed the publication of the paper, the Editor-in-Chief of Remote Sensing stepped down. He had this to say: (PDF)
“After having become aware of the situation, and studying the various pro and contra arguments, I agree with the critics of the paper. Therefore, I would like to take the responsibility for this editorial decision and, as a result, step down as Editor-in-Chief of the journal Remote Sensing.
With this step I would also like to personally protest against how the authors and like-minded climate sceptics have much exaggerated the paper’s conclusions in public statements…” 
In fact, Spencer has a long history of making erroneous statements. Here is a list of some of his blunders.
Spencer is a believer and supporter of intelligent design and a signatory to An Evangelical Declaration on Global Warming, which states that "Earth and its ecosystems – created by God's intelligent design and infinite power and sustained by His faithful providence – are robust, resilient, self-regulating, and self-correcting". In the book The Evolution Crisis, Spencer wrote, "I finally became convinced that the theory of creation actually had a much better scientific basis than the theory of evolution, for the creation model was actually better able to explain the physical and biological complexity in the world. [...] Science has startled us with its many discoveries and advances, but it has hit a brick wall in its attempt to rid itself of the need for a creator and designer."
So, from where I stand, I see someone who has rejected science in favor of creationism, has rejected climate change on a religious basis, has repeatedly made erroneous claims and has falsified his research in order to obtain the results he wants. This is not a good starting point.
But, let's take a look at his claims that he has posted on his website (provided above as the challenge).
It doesn't take long to find a misleading statement:
It is interesting to note that, even though carbon dioxide is necessary for life on Earth to exist, there is precious little of it in Earth’s atmosphere. As of 2008, only 39 out of every 100,000 molecules of air were CO2, and it will take mankind’s CO2 emissions 5 more years to increase that number by 1, to 40.
Here he has altered the numbering system to make it look as though they are insignificant. CO2 levels in the atmosphere are measure in parts per million (ppm) and the current level is about 400 ppm. To go from 390 to 400 ppm in five years is an increase in CO2 levels of about 2.5%, or about .5% per year over five years. This is much more significant than the increase of "1" that Spencer refers to. One what? If you had one dollar and it increased by one dollar, that would not be much. But, if you were talking about billions of dollars and it increased by "1", that is a much different story. Spencer is being deceptive by not putting the increase in context. Why would he need to do that if his claims are valid?
The basis for all of Spencer's claims is his claim that the climate sensitivity is much lower than accepted by the climate science community. A little explanation is needed here.
Warming (or cooling) is a function of radiative forcing. This is simply the difference between what comes in and what goes out. If more comes in than out, then we have warming. If more goes out than comes in, we have cooling. The big question is just how much change in temperature will occur when we have an imbalance in the radiative forcing? This is called climate sensitivity. If the sensitivity is low, then there can be a large change in the radiative forcing and there will be little change in the climate temperature. The higher the sensitivity, the more change in temperature will be observed for a given imbalance in the radiative forcing.
The IPCC uses the 'equilibrium climate sensitivity' (ECS), which is, basically, how much the global average temperature would change with a doubling of CO2 in the atmosphere. The Fifth Assessment Report (AR5) stated there is a high confidence in that the ECS is extremely unlikely to be less than 1 degree Celsius, medium confidence that it is likely between 1.5 and 4.5 degrees C, and very unlikely to be greater than 6 degrees C. Reducing all of the 'likely's and 'unlikely's gives an ECS of somewhere around 3 degrees C. What this means is that, according to the research cited in the report, if we double the amount of CO2 in the atmosphere we will most likely see a warming of about 3 degree C.
Spencer disputes this figure and believes it to be much lower. (Note: On his page, Spencer states the accepted value is between .25 and .5 degrees C per decade, this is equivalent to 2.5 to 5 degrees C per century and is consistent with the figures I quoted above, with the exception that I don't believe there is a time-span on the IPCC calculations. They just refer to a doubling of CO2 levels, no matter how long, or short, a period of time it takes to do that.)
On his "Global Warming 101" page, Spencer makes a curious statement when he says we have increased the greenhouse effect by about 1%. What he is referring to is known as the 'enhanced greenhouse effect'. Again, he has altered the way it is normally stated to make it sound different. The way it is normally stated is that our greenhouse gas emissions act is if the solar radiation has increased by 1%. To see how this is significant, consider this: the solar input is about 10^25 joules of energy per day. An increase of 1% is an additional 10^23 joules of energy. The entire world population uses about 10^21 joules of energy per year. So, the extra amount of energy we are storing in the atmosphere EVERY DAY (with that 1% change) is more than what we would generate, as an entire race, in 100 years! That is much more significant than just saying we increased greenhouse efficiency by 1%.
This all leads into Spencer's calculations and he has a paper on his website about his calculations on climate sensitivity. This one is dated 2008. He also published the very controversial paper in 2011 on this issue (see the quote from DeSmogBlog above). In his papers he basically claimed there was actually a negative feedback with CO2 in the atmosphere and he concluded that the climate is not sensitive to the greenhouse effect.
Spencer made a very serious error in his work, and it is so big I have to believe it was done intentionally. He did not include a realistic ocean in his climate models. Nor did he include the El Nino Southern Oscillation (ENSO) which is a major driver of climate variability.
In the end, it was found by independent reviewers that Spencer's claims were invalid.
Since his work was invalid, his claims about climate sensitivity being low were also invalid, and his claim that man made global warming is not real is also invalid.
After reviewing his work, I agree. This is not evidence that man made global warming is not real.