One big disadvantage to functional programming is that on a theoretical level, it doesn't match the hardware as well as most imperative languages. (This is the flip side of one of its obvious strengths, being able to express what you want done rather than how you want the computer to do it.)
For example, functional programming makes heavy use of recursion. This is fine in pure lambda calculus because mathematics' "stack" is unlimited. Of course, on real hardware, the stack is very much finite. Naively recursing over a large dataset can make your program go boom. Most functional languages optimize tail recursion so that this doesn't happen, but making an algorithm tail recursive can force you to do some rather unbeautiful code gymnastics (e.g., a tail-recursive map function creates a backwards list or has to build up a difference list, so it has to do extra work to get back to a normal mapped list in the correct order compared to the non-tail-recursive version).
(Thanks to Jared Updike for the difference list suggestion.)
