This is one of those posts meant for a Google search... hence the title (I tried to include things I searched for when debugging this issue).
Scenario: You have a TextField that has a style sheet applied to it. It is being dynamically updated with HTMLText. The text that is being inserted contains "a" tags for links.
Problem: When you mouse over the TextField the links move. Some would call it a jump, others a wiggle. Regardless, they move and your client does not think its funny that you call it a feature.
Failed Solutions: Remove Hover tag, doesn't help. Use a style class instead of applying it to all "a" tags... nothing. Use an external stylesheet instead of an AS class... nope. Baseball bat to monitor??? probably not going to help, but worth a shot.
Proper Solution: Stan here at the basement noticed that the AntiAlias on the Textfield was set to Advanced and concluded that maybe the text was changing due to the antialias. DING DING DING! Stan nailed it. He changed it to Normal and we no longer had jumpy/wiggly text links.
Side Note: This same issue will have a tendency to crash your browser if you have Flash player 10.0.12 and are running Firefox or Safari (maybe IE... not tested). It was very strange, the browser would not crash in the latest Flash 9 and it also worked in 10.0.22. It just really hated page changes in 10.0.12. When I went to test Stan's fix to the text bug, we realized that it also fixed our browser crashing bug.
Sooo, long story short, if you are using HTML text and your browser is randomly crashing or text is randomly jumping then you may want to turn off Advanced AntiAlias.
Hope that helps to whoever is unlucky enough to follow our in our footsteps.