You can use a DSO as a spectrum analyzer, but you'll have to spend a whole lot to get a bandwidth equivalent to that of even the most basic spectrum analyzer. Good spectrum analyzers also have very good dynamic range.
What might be interesting would be to make a spectrum analyzer by connecting something like a modified satellite or cable TV tuner to a low cost scope and having a PC control the whole thing. (Add further stages of downconversion and you might be able to use a sound card, although it would take longer to perform a sweep.)