What it boiled down to was that the js script was delayed in execution after clicking a checkbox: You'd click on the checkbox and nothing would happen. Then you'd click on something else, and the script would wake up and hurry to the bus stop.
After a bit of poking around, I found the problem: for reasons that escape me now (probably taking the lead from another script meant for use in a combo box), I was using an 'onModify' event to trigger my script, rather than 'onClick'. The problem this was cauing me arises in the way that different browsers handle these events.
Firefox thinks you change the content of a checkbox when you click on it, so it runs the script immediately.
Explorer, on the other hand, decides that changes to data should be acted on when the control has lost focus (and no one's looking), so it waits.
Solution: use 'onClick' whenever you wish to react to changed content of a checkbox.
One is inclined to give in to the temptation to knock IE6 because it's the done thing but, to be honest, I couldn't call the IE behaviour explicitly wrong and I don't know what, if anything, the standards say about when event handling should occur.