Two viewers complained that Panorama exaggerated the grounds for concern and wrongly suggested that Wi-Fi installations give off higher levels of radiation.
A further complaint suggested that the programme misleadingly presented an experiment to test whether certain people were hypersensitive to such radiation.
Professor Michael Repacholi, who appeared in the programme, also complained that the scientific issues had been presented in an unbalanced way, and that the treatment of his own contribution to the programme was unfair.
The BBC ruling found that it was legitimate for Panorama to focus on the public health issues raised by Sir William Stewart, chairman of the Health Protection Agency.
It also found that the results of an experiment on electro-sensitivity were correctly represented as inconclusive. However, the BBC report also identified a number of failings.
"The programme included only one contributor (Professor Repacholi) who disagreed with Sir William, compared with three scientists and a number of other speakers (one of whom was introduced as a former cancer specialist) who seconded his concerns," the ruling said.
"This gave a misleading impression of the state of scientific opinion on the issue."
Stewart claimed in the programme to have found evidence that low-level radiation from devices such as mobile phones and Wi-Fi could damage health, and called for a review.
The claims prompted a council body in north London to call for Wi-Fi use to be suspended in schools until an investigation had been carried out.
"I quite frankly think we are frying children's brains," said Labour councillor Emma Jones of Bruce Grove.
However, following the broadcast, a number of experts came forward to dismiss the claims.
Ben Goldacre, a doctor who runs the Bad Science website, stated that the programme makers had made melodramatic, misleading television instead of an informed documentary.
"In 28 minutes of TV you could have given a good summary of the research evidence so that people could make up their own minds. But that would not get you as many viewers," he said.
Les Hatton, a columnist on vnunet.com's sister title IT Week, wrote: "Many readers may be feeling that they need to wear tin-foil hats following the Panorama 'exposé' and the supposedly harmful effects on children caused by wireless networks.
"All I can say in reassurance is that this sort of mathematically dysfunctional scare-mongering drivel really makes me cross."
12 of the 32 stars observed feature rings and gaps that are usually carved by planets in the process of formation
Overhaul to parachuting system and the ability to export clips from replays also coming to PUBG
The experiment is currently underway at South Korea's Yangyang Underground Laboratory
Exoplanet HAT-P-11b is located about 124 light years from Earth