Don't know if this will help exactly with what you want but under the selection filters you can uncheck everything except "traces". Then you should be able do a mass selection and all your traces will be selected where you can then simply delete them.
Again not sure if that's what you're looking for. I'm not sure I understand what you mean by undo any nets that aren't fully connected. Do you mean delete the traces for which the rats nest has only been partially been routed?
Another strategy is using the "e" command/keystroke to progressively select more and more of the trace. Doesn't traverse vias I don't think nor does it traverse serpentine traces.