I've seen the same type of thing happen when I have 'routed pad thermals' unchecked and PADS puts a thermal on my routed connection anyway. What happens is that the trace goes to the pad but there is still a very short disconnect line connecting the trace to the center of the pad. I believe if you turn off all layers and have <View><Nets>(unrouted details checked) you will see the short disconnecting lines that are causing the problem.
The solution is to select the pad and then start routing. Connect the new trace to the old trace and your connectivity error will go away. You need to do this for each pad, unfortunately.