Professional bodies and opposition politicians pointed to the "extreme pressure" the health service is under as the data was published showing patients are waiting too long for both emergency care and planned operations.
One treatment time goal has been missed for the first time since it was introduced in 2011, while the Scottish Government's law promising patients will receive the procedures they need within 12 weeks is still being broken - with performance sliding backwards.
There were also signs social services are struggling as the number of patients delayed more than four weeks in hospitals when they were ready to be discharged to community care packages has risen 293 per cent in a year.
Neil Findlay, health spokesman for Scottish Labour, said the release of the figures made for a "worrying day" and called for Health Secretary Alex Neil to resign.
Mr Neil last week survived a vote of confidence at Holyrood over claims he abused his ministerial power to retain services in his Lanarkshire constituency, against health board advice.
He said: "If Alex Neil won't resign because he broke the Ministerial Code over his direction to overturn a decision affecting Monklands Hospital, then these terrible statistics showing the NHS breaking under pressure should be reason enough for him to go. Unfortunately for both patients and staff, Alex Neil will never accept responsibility for what is happening under his watch."
Significant progress was made in Scotland cutting NHS waiting times and delayed hospital discharges in the first decade of the new millennium.
However, more recently the statistics suggest hospitals have found it increasingly difficult to deliver government promises.
Waiting times in A&E departments have caused particular concern and delays of 12 hours or more have been slashed since the winter of 2012-13 thanks to a national action plan, the investment of millions of pounds and a relatively mild flu season.
But nine NHS boards are still missing the target to deal with 98 per cent of patients within four hours and, according to the new figures, in NHS Greater Glasgow and Clyde, one in every 10 people queues for too long.
As the figures were released yesterday, Mr Neil announced that the number of consultants employed by NHS Scotland is at record levels. However, there are also 324 consultant vacancies - a 60 per cent increase in 12 months - and the highest figure in records dating back 10 years. Worrying gaps in medical cover are among the issues raised by a damning investigation in high death rates in NHS Lanarkshire hospitals.
A British Medical Association Scotland spokeswoman said: "Whilst the government is painting a picture of a well-staffed NHS, the reality is that doctors are working under extreme pressure and workforce shortages and high vacancy rates are significant contributing factors to this. Medical staff are working under considerable strain."
Use of agency nurses to fill gaps on wards also increased by 35 per cent last year, with the total bill reaching £9.3m.
Theresa Fyffe, director of RCN Scotland, said: "NHS Greater and Glasgow, which made significant cuts to its nursing workforce, has increased its reliance on bank staff by nearly 17 per cent over the past year."
Jim Hume, Scottish Liberal Democrat health spokesman, called for an explanation.
Scottish Conservative health spokesman Jackson Carlaw said the new figures suggested waiting times for treatment "are the worst for a number of years and that is a damning indictment on this Scottish Government".
A Scottish Government spokesman said consultant vacancy rates were lower now, than in 2006 at 6.5 per cent of all posts.
Mr Neil said tackling delayed discharges was one of the main reasons the NHS and social care services were being integrated.
He said there was "no question" that the NHS is making sustainable progress cutting A&E waiting times, but some boards were facing problems delivering planned treatment in line with targets.