Originally Posted by mathieu
Anyway, I'm still interested in knowing whether or not you should let the bottles air dry.
You don't need to let the bottles dry before filling. You should be using a sanitizer rather than a cleaner, though.
LD Carlson is a no rinse cleaner so you shouldn't have any problems from using it, but there may be some beasties hiding in your bottles. Probably not, so don't worry about it - but look for a sanitizer for next time.
I use Starsan, I've used a bleach solution, and lots of others use Iodophor or sterlize bottles in the dishwasher or oven. Do some searches and you'll turn up lots of different methods that all work.