In the 1970s one of the more studly work boys at Camp Galilee used to wear a t-shirt with a cartoon of a bee on it and the caption "Eat Your Local Honey." Turns out the message is still the same.
In order to be considered proper honey, it needs to a) not be ultra-filtered, removing the pollen and b) have no additives. Most national and store brand honey available at supermarkets, big box stores, and discount drug stores, doesn't pass muster.
Why do we want our honey to contain pollen? because it's how we can tell where it's from. Much of the honey tested was probably imported from China, and ultra-filtered to obscure its origins. Estimates suggest that the FDA inspects only about 5% of honey imports. Unregulated and uninspected imported honey can contain all kinds of toxins and additives you don't want.
Honey from Trader Joe's, from natural food stores, and honey labeled organic had a better chance of being the real thing. But buying it from your local bee-keeper is still your best bet. If you are concerned about pollen allergies and eating honey for that reason, local honey is a better choice anyway.
I know, it's expensive, and getting worse what with colony collapse disorder and the other environmental pressures on bees. Clearly a situation where the solution is to eat the good stuff sparingly.