It does seem to be fairly universal on the document, which is exactly what I frequently see happen when I shrink a file.
In this case, I suspect that they first expanded it, to make it easier to edit, then shrunk it back after they were done.
When I open up the WH birth certificate document (042711obamabirthwsj.pdf) using Adobe Reader, and then expand to the region you have shown with the word "Hospital" (Box 6c), I don't get any grey-scale pixels on the "ospit" as you are showing. Mine are either full black or not at all. Furthermore, the "ospit" letters have pixels that are half the size of the pixels on the "H" and the "al".
I am using Adobe Reader 8.2.6 on a Win7 machine, with a screen resolution of 1920 x 1080.
Can you just repeat for me one more time in more detail exactly what steps you took to get grey-scale on the whole word "Hospital"?
Thanks