I believe 10.1 has serious problems with feature layers.
Another issue I'm having is that if you move a layer from one data frame to another, tools do NOT work on it at all, the claim being that the layer does not exist. It is trying to access the layer in the data frame from which you copied the layer and since that frame isn't the active one, it can't access THAT layer. This I think is quite reproducible. When I move a data layer to a different data frame, I HAVE to rename it.
Also, and this is a very old problem that I had hoped would be fixed by now. If you have, say, three layers with the same name (I know... you shouldn't) and pick the third one as input into the tool, the tool process the first layer with that name. Not a bug, but something that reflects a certain, shall we say, lack of sophistication regarding the relationship between a particular layer and its associated data on disk.