Yes, anthropogenic global warming is sizable and real, and most of our climate models need to be seriously reworked.
Greenhouse gasses create a heat flux at the surface, and this can only be balanced by storing the heat in the ocean, melting ice with the heat, or by raising the surface temperature until the extra heat is radiated into space. Currently, ice melting is negligible (at least in comparison to the heat budget), and about half the greenhouse heat flux is stored in the ocean, which means that equilibrium greenhouse warming for today's levels of greenhouse gasses will be roughly twice what it is today, and that's before adding additional forcing from albedo feedback from melting arctic ice.
This conclusion is robust regardless of the model used, though different models have different cloud effects which give different numbers for the size of the warming. The average global outgoing IR radiation must balance the increased heat flux, so the area integral of the fourth power of temperature must increase by a certain amount, and this is usually simplified to talk about the global average temperature. The problem is that heat storage in the ocean isn't constant with time, and neither is global heat transfer, so the actual effects for particular regions can be rather strange. As an example, take the instrumental temperature record for Alaska which is clearly a step function temperature change in 1977.
Climate models don't just calculate from basic physical laws, but use phenomenological rules verified over time. This of course can create problems if you go outside the range of parameters where those rules are valid. As an example of this, hurricanes are too small to be represented in the current models, and as a result the mixing caused by them is replaced by a constant factor called background mixing, which clearly will lead to too little mixing when hurricane strengths increase.
Most of the current climate models have a serious problem with not enough internal climate variability over mulit-decadal time-scales. They can't produce the constant drop of the salinity of the North Atlantic from the start of good measurements in the 1950s until 2004 (at least with the right size). They can't produce the 80% drop in deep water production in the Antarctic in the past 50 years or so compared to what it must have been over the past few centuries They can't produce the huge annual variations in the North Atlantic thermohaline circulation that we've been able to measure recently now that we have fixed buoys recently placed and constantly measuring it. And, glaringly, most of them can't ever produce the >15% drop in sea ice extent this year from the previous record.
The coupled sea-ocean models are really just need a few tweaks, and one of them actually produced a chance of the sea ice extent drop, but they still suffer from a lack of a good long observation record for model validation. The glacier models really are just a wild guess and most glaciologists aren't particularly confident that they aren't off by nearly an order of magnitude and believe that there's at least a very small chance that the global ocean rise over the next century could be 2-4 meters. In addition to the coastal flooding, This would cause a huge shift in ocean circulations.
What people actually want isn't so much a climate forecast of the average temperature and rainfall at their location over many runs of a climate model with the correct forcing, but the significantly different numbers of what the average temperature and rainfall are likely to be for the next 1, 5, 10 and 30 years, given current conditions of a PDO positive phase since 1977 and very high arctic thermohaline circulation since 2004, etc., etc.
So, be confident that the Earth will be warmer. As the years go by and we keep pumping CO2 into the atmosphere faster and faster, the chances are that almost all locations will be warmer. The temperate rain belt seems to shift towards the poles in just about every model. Other than that, the models' climate projections are more likely than not, but I'm not going to feel very confident in them until the models get tweaked again.
