Alex McKay, the council's director of education, said some of the greatest difficulties are in special education where appropriate qualifications and experience are often thin on the ground. The authority has also had problems with cover for English, languages, business studies and computing.
"You can run into problems pretty quickly," he says. "Heads are faced with difficult decisions."
Mr McKay, a member of the Scottish Executive's working group on teacher supply, adds: "It's a market that is much more difficult to read than 10-15 years ago when you could put X number of students into training and expect X number to take up work in schools.
"Now young people are emerging from training with greater opportunities. Some go to England, some to the Continent, and it can make quite a significant difference. The supply group is trying to gain a better understanding of the market."
He warns: "I think we are operating too close to the margins in terms of total teacher availability. But there is a pendulum. A year or two ago, people could not get jobs. So it's a complex picture."
Mr McKay is not certain that creating a pool of permanent supply teachers will be attractive to young people who are more mobile than ever.
And he is surprised parents do not complain more often about the effects of staff changes. "If research was done on how it affects learning, some schools could find the results quite worrying."