Here is some of the problems with computer models.

"Professor", you really should read past the first page.

"Chapter 5: Recommendations
1. Separate the uncertainties in climate forcings from uncertainties in the climate
response to forcings.
The simulations of 20th century (20CEN) climate analyzed here show climate responses
that differ because of differences in:
• Model physics and resolution;
• The forcings incorporated in the 20CEN experiment;
• The chosen forcing history, and the manner in which a specific forcing was applied.
• Model initial conditions.
We consider it a priority to partition the uncertainties in climate forcings and model
responses, and thus improve our ability to interpret differences between models and
observations. This could be achieved by better coordination of experimental design,
particularly for the 20CEN simulations that are most relevant for direct comparison
with observations.
2. Quantify the contributions of changes in black carbon aerosols and land use/land cover
to recent large-scale temperature changes.
We currently lack experiments in which the effects of black carbon aerosols and LULC
are varied individually (while holding other forcings constant). Such “single forcing” runs
will help to quantify the contributions of these forcings to global-scale changes in lapse
rates.
3. Explicitly consider model and observational uncertainty.
Efforts to evaluate model performance or identify human-induced climate change
should always account for uncertainties in both observations and in model simulations
of historical and future climate. This is particularly important for comparisons involving
long-term changes in upper-air temperatures. It is here that current observational
uncertainties are largest and require better quantification.
4. Perform the “next generation” of detection and attribution studies.
Formal detection and attribution studies utilizing the new generation of model and observational
data sets detailed herein should be undertaken as a matter of priority."

"In Chapter 5, we seek to explain and reconcile
the apparently disparate estimates of observed
changes in surface and tropospheric temperatures.
We make extensive use of computer
models of the climate system. In the real world,
multiple “climate forcings” vary simultaneously,
and it is difficult to identify and separate the
climate effects of individual factors. Furthermore,
the experiment that we are performing
with the Earth’s climate system lacks a suitable
control – we do not have a convenient “parallel
Earth” on which there are no human-induced
changes in greenhouse gases, aerosols, or other
climate forcings. Climate models can be used
to perform such controlled experiments, or to
simulate the response to changes in a single
forcing or combination of forcings, and thus
have real advantages for studying cause-effect
relationships. However, models also have
systematic errors that can diminish their usefulness
as a tool for interpretation of observations"

"This “noise reduction” aspect of AMIP runs
has been exploited in efforts to identify human
effects on year-to-year changes in atmospheric
temperatures (Folland et al., 1998; Sexton et
al., 2001) and volcanic influences on surface air
temperature (Mao and Robock, 1998).
One disadvantage of the AMIP experimental
set-up is that significant errors in one or more
of the applied forcing factors (or omission of
key forcings) are not “felt” by the prescribed
SSTs. Such errors are more obvious in a CGCM
experiment, where the ocean surface is free to
respond to imposed forcings. The lack of an
ocean response, combined with the masking
effects of natural variability, make it difficult
to use an AMIP-style experiment to estimate
the slow response of the climate system to an
imposed forcing change ."

"The CGCM experiments of interest here involve
a model that has been “spun-up” until it reaches
some quasi-steady climate state . The CGCM
is then run with estimates of how a variety of
natural and human-caused climate forcings
have changed over the 20th century. We refer
to these subsequently as “20CEN” experiments.
Since the true state of the climate system is
never fully known, the same forcing changes
are applied n times, each time starting from
a slightly different initial climate state. This
procedure yields n different realizations of climate
change. All of these realizations contain
some underlying “signal” (the climate response
to the imposed forcing changes) upon which
are superimposed n different manifestations
of “noise” (natural internal climate variability).
Taking averages over these n realizations yields
less noisy estimates of the signal (Wigley et
al., 2005a).
In a CGCM, ocean temperatures are fully predicted
rather than prescribed. This means that
even a (hypothetical) CGCM which perfectly
captured all important aspects of ENSO physics
would not have the same timing of El Niño
and La Niña events as the real world (except by
chance). The fact that ENSO variability – and
its effects on surface and atmospheric temperatures
– does not “line up in time” in observations
and CGCM experiments hampers direct
comparisons between the two ."

"This does not diminish the
importance of other climate forcings, whose
global-scale contributions to “differential
warming” have not been reliably quantified
to date.
Examples of these “other forcings” include
carbon-containing aerosols produced during
fossil fuel or biomass combustion, human-induced
changes in land surface properties, and
the indirect effects of tropospheric aerosols on
cloud properties."

Source

Seems that there are plusses and minusses in all computer models, but like Pop Tech said, any minusses and the models are junk. 

Very glad to hear you have an open mind.  I always broach this subject with a certain degree of trepidation here, knowing full well I will likely draw the ire of various individuals.

There is not "earth equation" -- there are, however, a known set of of so-called state equations that do in fact provide an exact (quantitative) description of the dynamics and thermodynamics.  Most of it is classical physics (conservation of mass, energy and momentum; ideal gas law; hydrostatics; cloud microphysics; etc.), although not all of it -- radiation obviously draws upon quantum theory.  I cannot emphasize enough that these models represent the very best of our capacity to understand the behavior of the real atmosphere.  Everything else, to some degree or another, requires various degrees of handwaving.

You are correct that one of the current limitations to these models is their ability to treat clouds.  They don't ignore them altogehter, but they do rely on parameterizations.  Regarding clouds, however, these have the capacity of acting as positive or negative feedbacks.  Lower level water clouds have high albedo and act as negative feedback (cooling mechanism).  However, high level ice clouds can act more as a positive feedback (warming) due to their absorption of upwelling infrared radiation.  Again, I am not a climate specialist -- this is stuff I learned in graduate level paleoclimate.

Don't worry -- you didn't get personal, so there's nothing to take personal.  And one other thing -- I am more of an empiricist -- models are fine and dandy, but they are not the real world.  But they do represent our best understanding of the real world, and I know the measurements show a long-term warming trend.