So - long story short, I started with one of the default layouts and heavily customized it using CSS. Everything works just fine in Chrome, but when the output is loaded in IE, the entire page shifts to the left, hiding a bit of the Nav panel on the left and leaving a white space on the right. It looks about the width of a scrollbar, and I tried forcing a scrollbar (as suggested by the folks over on stackexchange) but it hasn't fixed the problem.
Sadly, I cannot mandate that our clients use Chrome. Any ideas?
Without seeing the code, it's hard to gather what is going on. Let's take it from step 1: Does this only happen in the customised layout or also in the vanilla layout? Which layout is the base?
It appears to only happen in the customized layout. I started with Charcoal Grey.
UPDATE: I appear to have fixed it. I compared the vanilla layout css file to my customized one line-by-line and discovered that I must have accidentally deleted a background-image:url("top.png") line. Having added that back in, I can't make IE recreate the issue I was having.
Thanks to Willam van Weelden for suggesting I test whether it was just my layout!