Are there any known stability issues when using .NET 1.1 libraries in a .NET 4.0 application?
Come on, buddy, why on earth you would use NET 1 libraries in NET 4 application? NET1 is almost nine years old, you should use at least NET2 or better yet NET 35 libraries for what is worth.
We have used many .NET 1.0 libraries in different version of framework (any thing between 1.1 to 4.0) and have never experienced any issues. we currently use SQLDataProvider which I think was release a bit after .NET 1.0.
Then again it all depends on the code that is included in those libraries. I would spend some time to look for updated version of those libraries or even alternative, specially something that was written in 2.0 or higher just because of introduction of generics.
but otherwise, do some testing and you should be fine.
Generic answer is NO. You should be able to use .NET 1.1 libraries in a .NET 4.0 project witout any issues. But every library is different. Is it a custom dll? Does it use any COM components?