I have just upgraded my Inspire 1 with a Zenmuse X5 and an Olympus 14-42mm lens. The still photos are fine but the MP4 video is washed out of colour and lack of contrast. What settings should I be using to improve the output?
The colour depends what setting you have. Maybe if it's washed out, you're using D-Log or Cine D. Those two shoot with a wider dynamic range and tend to look whitish haze. They require colour correction at post editing and will look better as you'll get more details in shadows.
If you select None then you should have video straight out of camera that looks well coloured and good contrast. But you'll loose some detail in shadows.