Risk vs benefit of using LastPass on Chrome in OS X?
I don't have enough experience and knowledge of the LastPass folks to answer your questions. The dropbox issue is a non-issue if the data stored on the site was encrypted well before it ever was sent off your computer.

In general, I have different criteria for selecting software that is critical for me. Some random plug in, pictures, a cool app that doesn't store say, banking information. I'm all about giving people the benefit of the doubt.

My core operating system and my password generator/manager isn't time for that sort of experimentation. I am very happy using 1Password and understand their business model. Yes, for a time it was free, but it was obvious that they had a sustainable and reasonable pricing model. Now that they have (I hope) millions of users, they can charge a modest cost to ensure they have great response, great support and most importantly, great engineering. I will make more allowances for initial downsides when I believe more in the long term decisions of the company making my core tech and less likely to dabble in newcomer efforts (no matter how worthy they seem).

I would evaluate whatever software you choose by trying LastPass, 1Password and several others with fake data, but not trust your critical information to software until you are comfortable knowing who made it, how they secure data, and that they won't likely sell out to a low bidder at the first wave of $25k.  The value of millions of people to add to a corporate mailing list is attractive to owners that don't have an otherwise viable business model. I try hard not to be part of their short sell-off strategy by giving them my most valuable information for free.

I hope this helps you frame your decision and someone else that has gotten comfortable with LastPass weighs in with their take on your questions. It's a good one and high time more users start holding their authentication credentials a little closer and more securely between sites.