There is a recent paper in Preventive Veterinary Medicine about a study of Giardia in canine stool samples collected from urban green areas around Pisa, Italy (Papini et al). The authors went to parks and similar areas and collected stool samples off the ground. They then tested the samples for the presence of Giardia and (very importantly) tested the Giardia to determine whether they were types that typically only infect dogs or whether they were types also found in people.
They found that 31% of stool samples contained Giardia. That’s higher than in some recent North American reports. The number of Giardia cysts ranged from 2 to 1428 per gram of feces. Less than 1% of the Giardia were types that are of concern for transmission to people. Therefore, they concluded that parks pose a risk to dogs, since there is a good likelihood that dogs could be exposed to Giardia. However, the risk to people from Giardia found in these parks is minimal given the types that were found.
The risks to dogs and people can be decreased by the simple act of picking up poop.