2 QUESTIONS: 1) If I make changes to improve my quality score (changes that Google should notice right away, such as changing my ad to include the keyword), how long does it take Google to drop the minimum bid? 2) And is there anyway I can automatically know that it got lowered? (or do I have to manually go in a drop my bids to find out? - that could be a LOT of tedious work)
Regarding 2), if you make the Quality Score visible on the keyword level results, you can see the minimum bid next to each keyword, so you don't need to adjust the bids to find out. http://adwords.google.com/support/bin/answer.py?answer=21383 Regarding 1), it seems to vary - it can be hours or days. My guess, and it is no more than that, is that they review all of your Quality Scores at the same time, when it's your turn.
"1) If I make changes to improve my quality score (changes that Google should notice right away, such as changing my ad to include the keyword), how long does it take Google to drop the minimum bid?" More often that not for me, changes/updates take place the same day. Odd times it can take 2 or 3 days.