The boards here, and our bio and descriptions, accept HTML code. Quotation marks are used in code to define calls to specific files, and thus don't appear correctly when typed straight in.
This makes is very difficult to explain how to fix the problem, because in trying to show you the code, the board will convert my instructions to the HTML display. I'll give it a shot:
These are "straight" keyboard quotes (I put them in using the regular old double quote key on the keyboard)
These are "HTML" quotes (I put them in by typing an ampersand followed by the word quot with no spaces where the marks should appear in my phrase)
So, go into your descriptions and replace your straight quotation marks with this: (remove all underscores) _&_quot_ put it, with no spaces afterwards, where you put your opening and closing double quotes.
I tried it on my own profile bio and it displays quotation marks just fine. :)