I'm all for analyzing the problem scientifically, but, really, what do you think the IPCC reports are based on?
Regarding the weather question, this is a valid concern. There's of course a difference between predicting the weather, meaning the exact temperature and precipitation on certain days, and predicting climate, meaning mean quantities over the scale of years. It's true that for a chaotic system, it's difficult to predict the exact state of the system far in advance unless you have extremely good models and information of the current state. However, predicting the mean of a distribution is usually far easier. To what extent is this a problem with current weather models? I'm not an expert enough to know, but I'd suspect it has been tested.
Regarding the weather question, this is a valid concern. There's of course a difference between predicting the weather, meaning the exact temperature and precipitation on certain days, and predicting climate, meaning mean quantities over the scale of years. It's true that for a chaotic system, it's difficult to predict the exact state of the system far in advance unless you have extremely good models and information of the current state. However, predicting the mean of a distribution is usually far easier. To what extent is this a problem with current weather models? I'm not an expert enough to know, but I'd suspect it has been tested.