Dennis,
From the picture you included, it looks like those areas are being rasterized or flattened at a low resolution?? This typically means that an object below that portion of text is a raster or contains transparency. This could also mean you need a new driver:
Read HereHere's another bit of advice I found from an unknown author:
"Speaking from a Mac standpoint, don't use the obvious Export as PDF routine. You'll have one problem or another sooner or later. Just give up and accept the most common approach. Choose Print, then change your printer selection to Adobe PDF and choose Output Options. Put a check mark in the Save As File box, and then choose PostScript from the Format drop-down menu. Please try to ignore the PDF choice, and the large "Save As PDF" button at the bottom. Now, choose FreeHand MX from the main drop-down menu and make sure that everything is in order here - whether you want separations or a composite print, printers' marks, colors, page size, and so on. Then click Save. A PostScript file will be created. When it's done, you must run the file through Adobe Acrobat Distiller, and there you can select the degree of quality for the file. Note that you must have the "full" version of Adobe Acrobat to have access to Distiller - but it's more than worth the investment cost."
Illustrator does support the "halo". I typically create this appearance using the appearance palette. All you do is select the text, add a "new stroke" in the appearance palette drop-down menu and then drag the new stroke beneath the fill. You can then select the "fill" in the appearance palette and fill it with the color of your choice. Of course you can adjust the halo size by targeting the new stroke in the appearance palette and changing the stroke weight accordingly.
Nick posted a tutorial on how to do this once upon a time, but I can't seem to find the link.