Positioning of table cells is problematic. The usual solution is to leave the style of the td alone, and put a div in it which you make position:relative. Then place the content inside that div.
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Edit:
I don't know which effect you're after, but here's a jsFiddle demonstrating the problem: http://jsfiddle.net/ygP7k/5/
It has a table with little absolutely positioned divs in each table cell, that are supposed to align to the bottom right corners. It works in all browsers except Mozilla ones.
But here is an updated one with the extra divs as I mentioned: http://jsfiddle.net/ygP7k/7/
This works exactly the same, except that it also does the trick in Firefox.
Can you work with this? Does this answer your question?