Heh, hiding badly seems rather unlikely. A galaxy spanning race that can cross untold light years is not likely to make easy/simple/stupid mistakes often.
However, a self replicating probe might well be monitoring the earth, and watching for various milestones (fire, wheels, radio, spread spectrum, nuclear, fusion, stealth, inter planetary probes, plasma drives, etc). Certainly many things could be monitored passively, but occasional active monitoring might be justified.
Things like pestering military vehicles in relatively crowded seas (Off the coast of San Diego) to see what exactly we do when confronted with a unknown vehicle. What sensors do we use? How sophisticated are they? Do we risk the lives of fellow humans opening up on the unknown with multiple weapons?