I just watched a video by Scott Head - first part is his winter garden harvest, second is doing a bio-assay for herbicides. I am most familiar with Roundup but there is one new to me, Grazon, that is sprayed on pastures and it goes right through the cattle that are grazed on it and kills broad-leaf plants* when the composted manure is used on a garden. He has also found it in hay (not straw so far). I checked and there are 4 broad-leaf weed-killers approved in Canada for range management (broad-leaf weeds and especially tree seedlings), including Grazon, so this could be a problem here as well as in the US - and possibly other places too.
So to do the bioassay, he puts a bit of the composted manure in a pot, and plants a few bean and tomato seeds because they are very susceptible to damage. If they grow well the manure is not contaminated. Foliage curls horribly if the plant is exposed to Grazon. I don't know what it does with other herbicides, but it won't look normal.
I know the compost we get at my community garden is variable in quality, so this year I am not going to get it put on my plot, but just get a bit from the left-over pile and check it. If it is good I will use it. Same for the bags of manure I buy.
Theoretically if they are contaminated I could use the manure on my asparagus, corn and onions/garlic, but I would rather not eat potentially contaminated foods. I will give them to DD for her lawn. They will break down eventually.
*Basic botany: seeds can be monocots or dicots ("cot" is short for cotyledon, the seed leaf). Monocots have a single seed leaf, dicots have 2 seed leaves. So if you look at a seedling and it has one single shoot, like an onion or a corn plant, it is a monocot. If it has 2, like a bean, it is a dicot. Peas are dicots, but their seed leaves stay underground. Once we see true leaves, the veins in a monocot leaf are parallel, but the veins on a dicot leaf are not. Flowers - monocots have flower parts in multiples of 3, dicots have flower parts in multiples of 4 or 5. Of course fused parts can make this difficult to check, but the leaf veins are always a guide.