I don't see much of a difference between your before and after screen shots. What procedure did you do between the "before" and the "after"? When you say "save the video" do you mean "share it out" (export) it? Or clicking on the reset button to apply your changes? Is the text clear in the final exported movie? After you enter your text and Reset your changes, is the text clear at that point?
The issue may be related to this one font. Try changing fonts and see if that cures it. Also, go to Applications>FontBook.app and do a File/Validate fonts. See if this font is flagged as having any issues. While still in FontBook.app click on Edit/Look for Enabled Duplicates. If your particular font is duplicated then Edit/Disable the duplicate.
After you enter your text and then click on the blue Reset button the text will automatically get slightly bigger as the changes are set. Happens with all fonts.
Sometimes third party fonts (that are not Apple) can cause issues.
Try opening iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that
appears. iMovie will open in a new library. Reopen your old library to get back to your projects. See if that clears it up.
Also, try copying your media to a newly created project and see if that helps. To do that click on Edit/Select All, Edit/Copy, of the media in your project's timeline, and then Edit/Paste it into a newly created project. See if the font works there.
-- Rich