I did ask for a specific aspect of your choice.
In its absence, an overview:
Monckton makes a case that climate sensitivity, the amount that the global average temperature increases if CO2 doubles is much less than the IPCC estimate of 3 °C. Monckton reckons sensitivity is just 0.58K.
How does he come up with such a number?
He starts with an equation for forcing...so far so good.
Then he claims that the supposedly missing hotspot means that forcing has to be reduced by a factor of three. In doing this he misunderstands Lindzen (2007), But Lindzen (2007) does not say that CO2 radiative forcing is too high, "we can reasonably bound the anthropogenic contributions to surface warming since 1979 to a third of the observed warming, leading to a climate sensitivity too small to offer any significant measure of alarm".
Note that this is a statement about sensitivity not CO2 forcing.
Next Monckton turns his attention to sensitivity and argues it's too high as well.
Monckton proceeds to "prove" that sensitivity will be less than the value implicit in IPCC (2007).
In his "proof" he assumes there is no delay in warming (unlikely!) and McKitrick's data is correct (although he confused degrees with radians and his paper is totally unreliable), to arrive at his low value of sensitivity.
If we also assume that the IPCC forcing and feedback values are correct, then their value of sensitivity must be too high; Monckton comes up with a number 20% less. But in a previous section Monckton argued that the IPCC forcing value was too high by a factor of three. Yet if we we use Monckton's number, the IPCC value of sensitivity is too low.
Put simply, Monckton's paper arrives at conclusions that are not supported by its own maths.