The animation timelines become confused. Objects with a begin delay will remain in the last position before the reset button was clicked. Some flickering occurs. Eventually it resolves.
setCurrentTime is implemented smoothly in Firefox 17 and Opera 12
Thanks for filing this Matt. I looked into this and the fix involves fixing the fixme here: http://trac.webkit.org/browser/trunk/Source/WebCore/svg/animation/SVGSMILElement.cpp?rev=137709#L1142 (For posterity the upstream bug: crbug.com/166164)
FIXME is still present 10 years later.
<rdar://problem/97098635>