Google Android Market Knows....

The official Google Android Market knows what apps you have installed from the Amazon App Store. They won't show up in the Market's "My Apps," but if you do a search for an app and you happen to already have it from the Amazon App Store, it will tell you that you have it installed so you don't download it or re-purchase it through Google. You can open it, It will however not let you uninstall it through the Market. I thought that was interesting and helpful for people that have a lot of apps and forget what is installed on their phone. This does not work with apps downloaded from non app appstores like Getjar through websites. (The Android Marketplace did not show that I have Cut The Rope installed.)

This works on the phone app, not on your pc through market.android.com

9.14.11

I found another interesting feature of the Android Market showing what apps you have installed from the Amazon App Store. If the Google Market has an updated version, it will have the option to Update it! However, you WILL have to pay for it again (if it were a paid app to begin with.) Here's an example:
I "purchased" A Game With Balls when it was free from the Amazon App Store. It is currently at Ver. 2.1.4. In the Android Market, it is now at Ver. 2.2  An Update button is there and if you Update it, you are asked to "Accept and Buy."  Current price for A Game With Balls is .99  Interesting!