Sats were marked and delivered on time this year
A head teachers' union says it has received roughly 100 complaints from members about Sats "inaccuracies".
The National Union of Head Teachers said unfair marking and poor consistency were among complaints about the tests for 11-year-olds in England.
99.9% of the Key Stage 2 results were delivered on time this month after massive delays and marking problems last year.
Exams regulator Ofqual said it would consider any concerns schools had.
A marking fiasco in 2008 led to an inquiry and the resignation of the boss of the Qualifications and Curriculum Authority, Ken Boston.
The contractor hired to mark the tests, ETS Europe, was removed.
This year, only 11-year-olds sat the national curriculum tests after Sats were abolished for 14-year-olds.
The NAHT said around 100 head teachers had raised concerns about:
- harsh and unfair marking
- spelling marked wrong when right or marked right when wrong
- an overly-formulaic marking scheme which penalises creativity
- lack of consistency in marking composition
- inadequate care taken over marking
- clerical errors
Ian Foster, NAHT assistant secretary, said Sats' errors could put teachers' careers on the line.
"The bureaucracy and stress surrounding these outmoded tests, compounded by clear examples of poor or inadequate marking, can be dispiriting for pupils and parents," he said.
He said the stakes were high and errors could lead to flawed data being used to judge a school.
However, other teaching unions said they had not received a significant number of complaints about Sats results.
The NASUWT union said they were not aware that many concerns had been brought to their attention.
In a statement, Ofqual said: "This year there have been significant changes to national curriculum tests.
"As regulator, Ofqual will be listening to schools about any concerns that they might have.
"Every year schools raise issues with us regarding national curriculum tests and we are currently considering some of the comments we have received this summer.
"We will also continue our wider work into the marking quality of this year's tests with the aim of reporting later this year."