Is there any language as rich in different terms for fools as Yiddish? There seem to be as many as Inuit allegedly has for snow.
nebech (anglicized as nebbish): an innocuous, weak, or helpless unfortunate
shlemiel: a foolish person or simpleton
shlimazl: a chronically unlucky person
These aren’t just in alphabetical order. They’re also in pity order. You pity the nebech more than the shlemiel and the shlemiel more than the shlimazl.
The rule of thumb is that the shlemiel pours soup down the neck of the shlimazl. The nebech cleans it up. I would characterize Harpo as a classic nebech, Chico is a shlemiel. Groucho is something entirely different: a shnorrer. Not a fool.
More fools NSFW:
putz: a jerk (literally, the male sexual organ)
shmuck: same thing but worse. Not to be used in polite company.
The members of the Obama Administration are emphatically not shlemiels. They might however, be shmendricks. I will leave it to the interested student to point out examples of the NSFWs above in the Obama Administration (or any other, for that matter—the White House tends to be full of them).
Note: there are probably as many definitions of these words as there are people who use them.