I've got two older Oly DSLRs, an E-1 and an E-620. The issue is with the E-620 which focus hunts considerably with 14-54mm and 70-300mm lenses. I've tried its 3 focus modes, but it seems to have issues with each. This is odd as the E-1 although not lightning fast, doesn't really hunt.
I only can tell you about the E-620 in combination with the 70-300mm lens. It is the one lens that hunts the most, especially at the far end of the zoom (300mm). The kit lens 14-42mm is fast in focussing while the lens i use the most, the Sigma 18-50mm, is a tiny bit slower, i always think because its heavier, but does not hunt. As far as i know none of my other lenses hunt. I have no experience with using live view since 99,99% of the time i use the optical viewfinder. As mentioned by others this might be an issue. Otherwise: If you use C-AF with moving objects all my lenses can hunt. What settings do you use?