+3  A: 

Use Fiddler and compare the differences in the data that Firefox and IE sends.

ZippyV
I've never used Fiddler before. After I initially logon to my site, I don't see any new listings for it under "Web Sessions". I can see all of my stack overflow activity.
RememberME
Nevermind, I got it. It was because the site is https.
RememberME
A: 

Got it to work, but I'd be interested to know if anyone can explain the "why".

Changed this

var dialog = $(this);
var form = dialog.find('input:text, select');
$.post('<%= ResolveUrl("~/company/post") %>', $(form).serialize(), function(data) { ...

to

var dialog = $(this);
var form = $('#popupCreateCompany').find('input:text, select');
$.post('<%= ResolveUrl("~/company/post") %>', $(form).serialize(), function(data) { ...

and it now works in IE.

I don't understand why it worked until last week and why it still worked for the contact from subcontract, but not the company from subcontract or the contact from company.

RememberME