The line is the way the transparency is rasterized in versions of PDF that do not support transparency.
In other words, the image is broken up into parts so that the transparency can be rendered into a bitmap of said image. The thin white line is the division between the rasterized...
Here is a site with some decent tutorials. Some are very rudimentary, but the others might help you grok the interface better.
http://www.sketchpad.net/illustrator.htm
Thanks for the tip on AI 10 and Tiger. I'll try reinstalling it.
Although I know of no resources ... there probably are some if you do a google search. Find a tutorial to help familiarize yourself with the the way AI works (I agree with you that it is a frustrating experience if you come from freehand).
In my experience, there are some things that have...