How to circumvent the market compatibility check? Sometimes I would like to install some App on my Notion Ink Adam but the Android Market says that my device is not compatible with the App. ATM I simply google for the specific App and search some file hoster where I can download the apk, but this has several disadvantages (you never know if it is a hacked version, you don't receive updates, etc).

Therefore I would like to simply tell the market that I know about the incompatibility, but I want to simply install the App anyway. Does someone of you know a solution?
Yes.  Unfortunately the Market appears to pull the version of Android directly from the system somehow, so I'm not sure how to get around apps that are limited by version.  However you can get around apps being limited to specific devices by editing your build.prop file.  See my answer here: How can I modify the phone model in build.prop to get unsupported apps?