You should be using a framework such as mootools to get rid of the many cross browser issues. MooTools "normalizes" alot of standard methods that some browsers may not have or is named differently.

But its also limited what I've run into with cross browser javascript issues even on more advanced tasks, the only potential thing I find is the Mozilla's .textContent vs. the .innerText one. Ofcourse you can say like:
var text = (element.textContent || element.innerText);

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