Brian,
Can you try a running average using shift registers? With this, if the latest point is over x% outside of the running average, then do not include it. Since your signal is "constant," then frequency filters will probably not help you. See the attached example in LabVIEW 6.0.2. The interesting part of this example is that you need to know what your expected value is. If this is unknown, then one must do a bit of statistics (probably through histogramming) to get an initial average value.
Randy Hoskin
Applications Engineer
National Instruments
http://www.ni.com/ask