You're right that signals like radio and TV broadcasts radiate essentially hemispherically (after all, they don't radiate through the Earth). However, many transmissions are quite directional, including some of the strongest ones. For example, the uplink to a satellite is highly directional to get the maximum EIRP. A radar signal is also highly directional and very often has a lot of power behind it. Radar signals also have characteristics that prove they're artificial, such as a high degree of frequency coherence and pulse repetition rates that change with different radar modes. Of all the signals radiated from Earth, those would probably be the most easily detectable. Once detected, it wouldn't be all that difficult to search a known location for other frequencies using more sensitive instruments.
Space/Science » in reply to Accidental detection is nearly impossible with any foreseeable equipment.
Not all radiated signals radiate spherically
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