The vacancies highlight the continuing struggle to recruit to shortage subjects such as maths and in high cost areas such as London - despite an overall rise in applications.
Recruitment expert John Howson expects maths to fall short of recruitment targets - 86 of the 96 secondary courses starting in September have spare places.
He also warned that modern foreign language courses may be in danger. This week 38 out of 81 French courses had vacancies, 22 out of 52 for German, and 28 out of 42 for general modern foreign languages.
Around three-quarters of religious education and music courses are also struggling to recruit. The figure is even higher for design and technology, while more than 60 per cent of information technology and geography courses have places going begging. In London and Essex this week, only 49 of 167 secondary courses were full.
But training providers are fairly upbeat, saying the Government's advertising campaign promoting pound;6,000 training bursaries has had an impact.
They are optimistic that most courses apart from maths and languages will only be short of a student or two, and are likely to fill with late applications by September.
Applications have risen - up 17.5 per cent for secondary postgraduate training, and up 18.9 per cent for primary in England and Wales, compared to August 2000. However, applications to undergraduate training - mostly primary - continue to fall, down 11 per cent last month to 54,108.
Peter Gilroy, the new chairman of the Universities Council for the Education of Teachers, said: "Most PGCE courses are likely to be full by September."
University admissions officers said graduates were continuing to apply later in the year. But applications were generally up, although the extra candidates were not always of the quality desired.
Jo Parsons, at King's College London, said: "We got 70 applications on Monday and are getting more applicants because of the advertising about the training bursaries, but it's getting the quality the tutors like."
Peter Dunn, a spokesman for Warwick University, said applications were buoyant and had doubled in some shortage areas, such as information technology.
"We're putting it down to better national advertising and the pound;6,000 training bursary. But we want to wait and see if these translate into real people taking up places."
A spokesman for Oxford University said recruitment there was good. But he suggested that research was needed to establish whether improved applications were down to the bursaries.