Why should the parser be expected to fix mistakes like that? It's possible to produce invalid HTML with just about any BBCode parser that doesn't use a state machine or some other complicated and slow solution like that.
Kinda related thread:
http://community.mybboard.net/archive/index.php/thread-12241.html
You can easily fix the problem by fixing your BBcode.
blah 1
quote:
test
blah 2
quote:
test2
blah 3
(The styling of
quote: is technically not supported =p)
/ 
