Can you show us your CF code that does the database INSERT? CFQUERY automatically doubles-up the single quotes in the query so that there are no SQL syntax errors, but what goes into the actual table row is just the single quotes. Using CFQUERYPARAM would also be advised to prevent injections. If we can see your code then maybe we can figure out what is going on.
You might want to write out to a text file (or use CFLOG if you also have access to the system logs) the contents of the form fields you are doing the database INSERTs on, just to verify that the strings you're passing to CFQUERY are what you expect, and are not already being doubled-up by some other code.