Detail of the case has emerged in a ruling by Judge Owens following a private family court hearing in Reading, Berkshire.
Council social services staff had asked her to make decisions about the boy's future.
She said no-one involved could be identified.
Judge Owens said the woman was a qualified nurse, but had an "extremely low range" of intellectual inability.
She said an independent social worker had prepared a report after observing mother and son.
"The independent social worker highlighted some of the concerns around [the woman's] ability to meet the needs of [the boy]," said the judge in her ruling.
"These include ... not feeding [the boy] in an appropriate position, not changing [his] nappy appropriately, and placing [his] nappy changing mat very close to a metal table leg when [he] was moving around on the mat."
Judge Owens said the social worker watched the woman, "spend about an hour holding [the boy] who was sitting in the Bob The Builder car".
The social worker had told how the woman "maintained limited eye contact and communication" and said the Bob The Builder toy car was "inappropriate" for his age because there was "a potential risk of [the boy] falling if [the woman] lost control of him".
To qualify as a nurse a student usually takes a degree course for which they generally need an A Level in biology or another science.
Courses are made up of work placements, lectures, exams and practical tests.