(1)  Monsanto's use of patents is a problem of government, not "corporate greed".  "Intellectual property" is a highly irrational construct that isn't based on Natural Rights - only on cronyism, lies, and blunt government force.  (The Complete Liberty Podcast just did an excellent series of episodes dealing with this very issue, in case anyone here is interested.)

(2)  All food is "genetically modified" through mutation, cross-breeding, and man's artificial selection - it's just a matter of degree.  Most of the plants we eat were drastically different just 10,000 years ago from what they are today.  Human beings evolved over millions of years to a very different "natural environment" than the one we live in today - an environment that would doom >90% of the world's current population to famine and extinction, and the survivors would face a miserable existence that is "nasty, brutish, and short".  Humanity was able to surpass all other animals through its ability to hack nature for its benefit, and modern genetic manipulation is just another logical step along the same successful path.

(3)  I agree that genetically modified foods may have some negative trade-offs and risks of side-effects, but they have positive attributes as well, which is the reason why they were created and popularized in the first place, in spite of all the fear-mongering and bad press they have caused.  A way of growing crops more cost-effectively, or in conditions where they were previously a lot more difficult to grow, or making them more resilient to pests or spoilage, etc all translate into better nutrition for billions of poor people for whom those crops were the best of all available alternatives.  People who let "perfect" become the enemy of "good" often end up with "evil" instead (speaking as a pragmatic compromise, not an ideological one), and millions of people may die if government regulations interfere in them being able to buy the best food that they are able to buy!

(4)  I'm a big fan of food labeling, transparency, and consumer activism, and the third can be used very effectively to encourage the former two.  I blame the current "government didn't ban it so it must be good" complacency of the average consumer on the government's inherently-corrupt quality assurance monopoly (ex. the FDA).  Without it people would be a lot more skeptical of every product they buy, and no reputable food manufacturer, distributer, or supermarket would ever be able to put out uncertified or mislabeled products without fearing a massive consumer backlash as the cost of scientific substance analysis continues to decline and access to information continues to improve.  "Given enough eyeballs, all bugs are shallow."

I think if they’re interested in (a) behaving ethically, and (b) changing their reputation for behaving otherwise, Monsanto needs to do change both their behavior and their method of response to criticism. 

Monsanto is behaving ethically - it is tasked with maximizing its profits for its investors within the confines of the law, which is exactly what it is doing.  It's the law and the inherently-corrupt government system behind it that is the problem.  If Monsanto wasn't doing it, some other corporation(s) would inevitably have taken its place instead.