We all think he is dumb, but if the office worker had not opened the package with poison in it (which he asked them not to) then he might have gotten away with it. It was through the office worker that the hospital and police were tipped off. I wonder what would have happened without that tip. Maybe it wouldn't have been traceable (he did google it).
Also, if he knew the office worker had seen the poison he probably wouldn't have used it. Instead, she closed it back up so he didn't know it had been opened.