This problem preceeds NuGet. If you have a project referenced in two solutions, and change assembly references in the project when it is open in one solution, of course it will change the reference path for that project when it is open in the other solution. This has always been the case, regardless of how the reference was changed (with NuGet or otherwise).
But the real problem is that when you do an update, the updated packages do not appear in the foo/packages directory right?
The simple solution is to move Common.csproj into a solution of its own, with its own references, packages folder, build and release process. Then create a NuGet package of your own with any relevant dependencies built into it. Then you can install your Common package into both Foo and Bar and then the Foo team is free to update to the latest version of Common as and when they are ready.
The main argument that I have heard against this is that you might want to step through the Common code while debugging, but this is no longer an issue with Visual Studio 2010.
The fundamental question you need to ask is who owns Common.csproj? Is it the Foo team or the Bar team?