The new Hillhead Primary School and Kelvin Park Early Years Centre opened last August following the merger of the Dowanhill and Willows Nursery Schools.
But parents claim the school's cutting-edge design has created a raft of problems for pupils.
One mum said her little girl slipped and fell into one of the school's fancy new toilets while trying to press the flusher.
Helen Stewart, whose three-year-old daughter Julia attends the nursery, said: "The design of the toilets, which look great but aren't practical, means that the smaller kids can't reach the flusher.
"They have to brace themselves against the edge of the dirty toilet seat.
"Julia slipped and fell in, which was very unpleasant for her.
"The height of the loo seats mean the boys are missing the bowl, leading to puddles of urine on the floor and terrible smells, and the kids can't go to the loo by themselves.
"The nursery staff are excellent, but they are Glasgow's highest-paid toilet attendants."
Parents also claim the toilets have no soap dispensers and the doors are so heavy that smaller children have been stuck inside them.
They also complain there are drainage problems with the playground.
And they claim there is so little storage space in the school that library books are kept in the disabled toilet.
Helen added: "There is more storage space in a Partick flat than there is in this nursery for 60 kids.
"We know all schools have problems but this is a flagship school that the council invites delegations to look around and it's full of problems.
"They have all the mod cons right but haven't managed the basics."
With a grass roof and classrooms facing east or west to catch natural light, the architects said they designed the building to be as environmentally friendly as possible
Green Party local councillor Martha Wardrop is backing the parents' complaints.
She said: "I am aware of some faults with the building's facilities and outdoor space.
"It has come to my attention that the landscaped playground has drainage problems and the toilets are not adequate.
"I am seeking assistance from education officials to ensure these matters are resolved and addressed as a matter of urgency."
A council spokeswoman said: "Discussions are taking place with the parent group and their concerns are being addressed but all sanitaryware conforms to care commission standards and a recent audit found no issues with the cleanliness of the nursery."