I don't think this bug has been reported, I hope this is the correct way to submit it. Thanks.
In this string,
s = "part1\"part2\'part3"
jEdit gets really confused. It doesn't properly recognize the escaped " or ' as just another character. Instead, you end up with 2 strings, "part1\" and the other which starts with "part3" and continues until the next ' in the file, so the syntax highlighting is all wrong.
If you change the closing " to ', the 2nd string becomes "part3" and the rest of the syntax highlighting appears ok, but this is misleading because your program is not syntactically correct anymore.
I'm using jEdit 4.3pre15 with Java 1.6.0_03.
Thanks, BTW outstanding editor!!!