The EU have acceptable "Maximum Residue Levels" of Glyphosate in foods: http://ec.europa.eu/food/plant/pesticides/eu-pesticides-data...

In wheat it is 10 mg/kg. (Page 5 from the above link).

This UK report: https://www.gov.uk/government/uploads/system/uploads/attachm...

found pesiticide residues in 90 of 96 cereal crop samples tested. However, it concluded that "None of the residues detected by the laboratory would be expected to have an effect on health."

A BBC TV programme covered this issue in 2014: http://www.countryfile.com/news/pesticides-found-over-60-uks...

>nobody is spraying wheat right before harvest

Glyphosate is sometimes used as a desiccant to alter the timing of wheat harvests, ensure even ripening, and to make harvesting easier. While it's not a widespread practice, it does happen in the US.

> Glyphosate doesn't last long enough to persist in plants and nobody is spraying wheat right before harvest.

Citation needed!

Snopes says that the underlying practice is real despite a lack of evidence that the glyphosate causes the ailments: https://www.snopes.com/food/tainted/roundupwheat.asp

This paper attempts to draw some kind of causual biochemical link between glyphosate and celiac through metabolic processes: https://www.ncbi.nlm.nih.gov/pubmed/24678255

Actually, it's a relatively popular harvesting practice for non-organic crops -- kill them all at the same time so they're all ready to harvest. Differs by region, but afaik in the US foods labelled as organic can't be harvested in this way.

The typical Glyphosate mix includes many other chemicals that do persist.