I'm formatting my thesis and need help with formatting tab leaders. I want the text that appears in the table of figures to be fully justified so it is all aligned. However, I want the tab leader (aka "...") in front of the page number to stick out from the justified text. So I need to format the text and tab-leader/page number separately. I can make the table of figures fully justified but that aligns everything, including the tab leader and page number.

Try putting a non-breaking (hard) space at the end of your figure captions. You can insert such a space with Ctrl+Shift+Spacebar.