Just got the A7 yesterday. The Auto ISO is not broken.
The Auto ISO range is user selectable from a minimum of 100 to a maximum of 25600.
At the default setting, the camera tries to use 1/60 as whenever possible in LOW LIGHT or indoor situations before going to a lower shutter speed. The shutter speed is higher in intense sunlight.
Anyone who wants to shoot higher shutter speeds in low light can force the camera to select higher ISOs by setting a smaller ISO range.
E.g. For a given daytime indoor scene with subdued sunlight through the window.
At Auto ISO range 6400-25600, the metering is 1/1250 f/2.8 ISO 6400
while at 100-25600, the metering is 1/60 f/2.8 ISO 320
For reference, the shutter speed at fixed 100 ISO is 1/20 at f/2.8.
The same thing works for outdoor shooting at small aperture in bright light.
E.g Auto ISO 100-25600, f/22 , 1/60 ISO 200
Auto ISO 1600-25600, f/22, the shutter speed is given as 1/500 at ISO1600
For reference, the shutter speed at fixed 100 ISO is 1/30 at f/22.
And if you happen to be coming in from the outdoors to indoors but left the aperture at f/22 in which case the metered scene is out of your selected ISO range, the camera will set the appropriate shutter speed lower than 1/60 so you still get the shot (if you're holding the camera steady and the subject is immobile).
So the conclusion is - set a higher & narrower Auto ISO range if you want to shoot at higher shutter speeds.
FWIW I'm basing my comments on using a Konica Minolta A mount AF slr lens + LAEA4 on the A7. The Leica M to Nex adapter hasn't arrived yet.