It seems that you are not able to extend or continue a route for instance after selecting the hand tool. I found a workaround by creating en new route and join them. Also system seems to hang after right clicking. I am on Basecamp version 3.02
This is one of the limitations we've identified with the route editing tools that we'd like to address in a future version of BaseCamp.
If you create additional waypoints you can either copy & paste or drag & drop them to the end of your existing route. Not optimal but it should allow you to extend the route as you intend.
The best solution for changing, would be to be able to drag the route around....
Every place you drag it too, gets a new waypoint, and then recalculated between the two neighbouring waypoints.
This would allow for quickly changing a route to preference, without first combersome going waypoint by waypoint, but by adding them.
Just have a look at google maps, adjusting a route is very well implemented at google maps.