IE will not load an ICO image into the browser unless its contentType is image/x-icon
.
I can confirm by looking at the network tab in Firefox that the contentType for the LinkedIn image is application/octet-stream
which would explain why IE will not show it while the Facebook image has a content type of image/x-icon
which IE likes.
There is nothing you can from the browser other than don't request an image that has that type set on its server. I'm quite sure that sites like LinkedIn will have other small images from there site that you can link to.
FYI, if you look at the linkedIn source for it's homepage, you will find a tag that points to http://s.c.lnkd.licdn.com/scds/common/u/images/logos/favicons/v1/16x16/favicon.ico which works just fine in IE (because it's an image/x-icon
).