Buenos Aires is generally as safe as any big city, and it is usually fine to walk around most areas even late at night (or as a lone woman) since many locals will be out on the street enjoying late night Argentine life. Take usual precautions against pickpocketing and bag snatching, particularly at bus stations, busy markets and on the subway, plus the following areas of the city: Constitucion, around the train station; east side of San Telmo; La Boca. You can report theft or other petty crime to the tourist police office at 436 Avenida Corrientes (interpreters available).
Hikers need to be well-prepared in Argentina – trails can be challenging, with few other hikers if you get into any problems. Weather can be very changeable too, especially in areas like Patagonia. Take all usual precautions in terms of water, sun protection, good maps and compass – and inform others where you are going and when you expect to return, if going off on a solo hike. Also carry extra layers of warm clothing, as temperatures can drop suddenly, particularly after sundown.
Demonstrations against austerity and associated economic/political issues are quite common, especially in Buenos Aires' Plaza de Mayo. There are ongoing protests in central Buenos Aires over what Argentina sees as the illegal British claim to Las Malvinas (The Falkland Islands), which remains hugely sensitive. Try to keep away from such demonstrations, and avoid speaking English loudly nearby to avoid unnecessary provocation.
You are unlikely to experience any real problems other than the crowds but if you want to avoid these keep an eye on local news.
To call the police, dial either 101 (24 police helpline in English) or 911.
Police can demand identification at any time, so always carry photo ID or a copy of your passport. And always be courteous and helpful to avoid discovering the labyrinthine intricacies of the Argentina legal system.