The statement "use strict";
will should not cause problems with IE8/9 insofar as the browsers will run the code. (It was designed that way, to ensure that there are no problems with browsers that don't implement strict mode)
External source: http://ejohn.org/blog/ecmascript-5-strict-mode-json-and-more/
This means that you can turn strict mode on in your scripts – today – and it’ll have, at worst, no side effect in old browsers.
NOTE: as Jeremy pointed out in the comments, there are some expressions which are technically valid but will fail in IE8 (for example: var x = {}; x.break = true
will not work in IE8 even though it will work in IE9).