Since IAT is somewhat sensitive to which pairing is made first, Inquisit presents them in different order to every other subject, so the first one gets flowers paired with good and the second participant gets insects with good and the like. Right?

As far as I can tell without looking at the actual script, this is correct.

In my data which I've gathered with the demo (yes, I will buy the license as soon as I get the money), it seems there's a huge difference between the groups that got first paired with A or B. A few questions:

1) I checked this for the subjects by looking at the first block after attribute practices in my ST-IAT. So there's TargetAleft for the first subject, but TargetARight for the second etc. Am I interpreting this correctly?

Hmm, not sure I understand the question. I would expect to see a notable difference when looking at a single block, since the block *is* different for the two subject groups. As you correctly noted, group A responded to a flower-good/insect-bad pairng while group B responded to the opposite insect-good/flower-bad combination in said block.

2) What's the correct way of estimating the size of this effect? I was told that correlating does not work in this case, so should I just check the means and perform ANOVA for significance of these, or?

Here's my take on this: In terms of ANOVA, 'pairing order' is just another two-level between-subjects factor. So, to test for any effects of 'pairing order', you include it in your ANOVA and see if it produces any significant main or interaction effects.

~Dave

P.S.: I can't believe I've wasted my seminal, 500th forum post to an IAT-related question - bummer...:-)