You are right that the models are continually advancing. However, to be honest, I think it is still true that he could show a graph of the sort that you describe. For example, the total “radiative forcing” from a doubling of CO2 levels is about 4 Watts per meter squared which is barely more than 1% of the total amount of radiation received from the sun (300 or so W/m^2, if I remember correctly). It is true that the absolute errors that are being made in some quantities are greater than this. I seem to recall a number like 20 W/m^2 for stuff involving clouds.
However, what is important to remember is that the climate models are run in a comparison mode…that is, they are run with greenhouse gases held constant and with greenhouse gases, say, doubled…and then the difference is considered. This looking at the difference cancels out a lot of potential “sins”. I.e., if you make the same 20 W/m^2 error in the cloud parametrization in both versions of the model, it will cancel out. The only potential problem would that would occur is if your change in greenhouse gas concentrations also changes significantly the error you are making in the cloud parametrization.
Admittedly, such possibilities can’t be completely ruled out. However, there are various ways in which we can gain more confidence in the models and their predictions. For example, the models are tested to see how well they “hindcast” the past climate over the past ~150 years, how well they simulate seasonal cycles, how well they reproduce the cooling produced for a couple of years following the eruption of Mt. Pinatubo in the early 1990s, and so forth. It is also noteworthy that there are lots of different models out there that make different assumptions in regards to clouds and other features that are parametrized…and so one can compare the models to one another. And, the recent climateprediction.net experiment varied various parameters in the models over what experts thought were realistic possible ranges and investigated how this affected the climate sensitivity. They found that none of the variations that they tried produced a climate sensitivity below 2 C for a doubling of CO2 levels (which is, in fact, the lower bound of the likely range in the latest IPCC report). They also found most of the variations produced sensitivities below ~4.5 C (which is the upper bound of the likely range in the IPCC report), although there was a long tail on the upper side with some parameter values producing sensitivity as high as 11 C! (Many other scientists think values this high can be ruled out by what we learn from paleoclimate studies.)
Finally, we are not relying entirely on modeling to predict the climate sensitivity. It can also be estimated from paleoclimate data, e.g., from the temperature change between the ice ages and the interglacial periods, along with an estimate of the natural forcings that produced these changes. And, these estimates seem to be in good agreement with the ranges produced by the models.
Just as a final philosophical note: Of course, it would be nice if the models were more perfect than they are. However, the fact is that, in general, science is not easy! I think non-scientists often get a somewhat naive view of science from what they learn, thinking that scientists deal in lots of certainty with very rigorous models and so forth. The harsh truth is that science makes great progress despite the fact that our ability to exactly simulate natural processes is often still quite imperfect in many ways. So, what you find is that with a controversial field like climate change or evolution, folks who are trying to provoke doubt amongst the public will latch on to the things in these fields that actually demonstrate various ways in which science isn’t as simple and ideal as people imagine it to be and use this to provoke doubt that we can believe the science. I often imagine that if quantum field theory went against certain people’s strong economic interests or political, philosophical, or religious beliefs then you would have people asking you how you can possibly believe a theory in which you have these strange infinities and you end up subtracting two diverging numbers in order to get a physical result for something like the mass of a particle!
Actually, the comparisons are usually made between previous times and the late 20th century. As you can see from here, the global temperature has climbed quite a bit since the 30s and 40s. Now, some people do point out that there was a pretty good rise between ~1910 and 1940 despite the fact that most CO2 wasn’t emitted until after 1940. This is true and, in fact, that rise is generally understood as being mainly due to solar influences along with a lack of major volcanic eruptions (that tend to cause cooling), along with probably a small contribution from rising greenhouse gas levels. As I showed you in a previous post, attempts to simulate the temperature variation over the last 150 years with natural forcings only do pretty well up until about 1970…but after that, the divergence is very striking and human forcings must be included to get good agreement with the temperature record (see here). The 20th century was really a century that marked the transition from the climate being dominated by natural forces to the climate being dominated by man.