Hmmmm. You are allowing, I hope, for some people other than the actual researchers to have good and well-founded opinions ?
At what level of "knowing the science" does one's ability to follow an argument, and compare it with another argument, appear?
I don't know ice. At some point, even the most well-educated layman is taking somone's word for it, right?
Let's say, for example, that someone (me) simply takes the researchers' word ... It's published and peer reviewed, it's stood for years now, and I just accept it.
Well, ok. Two things. First you haven't checked the calculations yourself, so how can you be sure? I know how peer review works---you send your paper to a journal, and they send it to a third (neutral) party. That person may or may not take their job seriously. And at the end of the day, it may be the person's graduate student who is actually reviewing the paper.
But ok. Say they take their job seriously. If that person has a vested interest in some particular science, or some particular result, they will push it. For example, I just got a paper back from peer review, and some of the comments were "You should cite authors X,Y, and Z...". (I'll forward you the email if you doubt me

)
All of this aside, the process basically works. And some peer reviewed research is published on both sides of the debate, which SHOWS it works. But the main place that science happens isn't in conferences or journals, its over coffee and in hallways of the geology department, etc. What you see in the literature is a highly technical account of all of these conversations, which is then trickled down through various pathways, into a form that most people can digest. But again, if you don't read the original literature, and do the calculations yourself, you really can't be sure of anyone's result.
And if you're not PART of that dialogue, then all you have is an outside account of what the debate really is. So you can say "So and so said this..." and I can say "Well, my so and so said that your so and so is wrong, so take that..."
The other thing is "I just accept it". Maybe this is a difference between physics and climate science. Physics is much more solid in the sense that anyone can do the calculations. If I don't believe, say, that the gravitational field inside a spherical shell is zero, then I can go and calculate it. I understand that some climate science models, and some sets of observations, may be so large and complicated so as to effectively prohibit anyone from repeating the experiment. If this is the case, then I really have no response.
So, for example, statements like
Taking this, and ignoring for the moment the fact that the boost is not linear, we have an anthro contribution of about 7% of the total heat trapped.
That is, I think, very obviously significant. Anything over 1% would be significant.
are almost completely meaningless. What does "7% of heat trapped" mean? How does this effect temperature, because heat and temperature are not the same thing? Does 7% more heat mean 7% more temperature? Why is 7% bad, but 1% ok? There's no substance to these statements, other than you can phrase it in a way that sounds like you know what you're talking about. (No offense intended, please!)
Now I am disposed, on this sketchy scientific background, to give more credence on less argument to claims of significance, and demand better argument from those claiming insignificance. And in fact just the opposite has been my experience - the anti-GW crowd has been featuring very bad arguments, full of logical flaws and spurious claims.
So is my position reasonable, although I am not a scientist or expert in the field?
Your position is certainly reasonable. But so is an equally informed layman on the other side of the debate, for the same reasons. The fact that sandy is aparently the only one arguing the other side, and that she is pretty ignorant of the differences between weather and climate, doesn't mean that there are not others like you out there. And when the two of you talk, you quote statistics at each other---the winner of the dialogue, if there is one, is the person who can counter each of your statistics with his own, +1. You can't disprove his statistics with anything other than statistics of your own.
I think my main objection to people talking about things like this is that they approach a scientific question in an unscientific manner. People attempt to justify a certain social agenda, based on science that may be still up in the air, and which they don't know. If the science was that solid, I wouldn't read in the paper about the number of famous climate scientists who are beginning to change their minds.
If you want to justify your social agenda on a "better safe than sorry" attitude, then fine. Honestly I feel that the anthropogenic global warming explanation holds more water than some of the other ``natural'' explanations I've heard, even though it doesn't sound like it

The fact is that we DONT know the dynamics of the atmosphere well enough, and we only really have one Earth. But make no mistake that the numbers you are quoting are still debated by scientists, over coffee and in hallways. Make no mistake that I can find equally convincing numbers, if I spent a few days with the literature, to completely disprove your case, I'm sure of it.