When an iron trapdoor is on the top half of a block, it will not be detected by the execute command. (note, '/execute @p ~ ~ ~ detect ~ ~ ~ minecraft:iron_trapdoor 0' etc. seemed to work if the trapdoor was on the bottom half of the block)

In the chat log, I was told that there was "Failure to detect as quickbeam1" (my username) when I attempted to run either '/execute @p ~ ~ ~ detect ~ ~ ~ minecraft:iron_trapdoor 0 say testing' or '/execute @p ~ ~ ~ detect ~ ~-1 ~ minecraft:iron_trapdoor 0 say testing'.

Therefore, I can conclude that there was no easy way to detect the trapdoor beneath the player's feet. This also applied to ordinary trapdoors