One school found that markers had made basic mental arithmetic mistakes which had cheated pupils out of dozens of marks. Staff at Amery Hill School in Hampshire found nine addition errors in 60 key stage 3 maths scripts.
Tim Griffiths, deputy head of Amery Hill, said: "We do not have time to go through every script checking the marker's maths, but it certainly raises serious doubts about the accuracy of the marks on our other papers."
Elsewhere, Derek Kennard, senior education adviser for North East Lincolnshire Counci, said: "Our schools have had to recheck their papers and found that pupils had been marked down by these silly mistakes, sometimes quite severely."
And Greg Marsden, headteacher at St Joseph's RC primary school, in Cleethorpes, has been told that the Northern Examinations and Assessment Board cannot find any of his school's 28 key stage 2 English scripts.
After two months he received a copy of the English test results, but the scripts are still missing.
He said: "My main concern is for the children who have grafted away all year and feel they have absolutely nothing to show for it. We now have our results, but have no way of querying low marks because we don't have the scripts to check the marks against."
Judith Besford, the examining board's project manager for key stage 2 and 3 external marking, wrote to the school: "I write to inform you that the scripts cannot be traced. NEAB is making every effort to trace the scripts and is involved with the marker, the named post office and the Parcelforce depot in seeking evidence of where the scripts might be."
A spokesman for the Qualifications and Curriculum Authority, which runs the tests, said: "All scripts are electronically tagged, so actually losing scripts is a very rare occurrence. They often turn up; it is just a case of tracking them through the system."