I think the meaning 'clerk' is someone who shoves paper, not just any employee.

According to my knowledge and my dictionary, a "clerk" can be any type of employee in an office or a shop.
It seems that there is a difference between British English, where it is more "office"-type and US where it is more "shop/salesman"-type...http://www.thefreedictionary.com/clerk

If you read the English pun again, it makes sense only as applied to a person who keeps the records. If such a person suffers from sticky fingers, flipping through papers is awkward. This is a wink at the profession, who like to drag affairs to nausea.
I am telling you this because I think the EO translation diverges too much.

It may also refer to US clerks, ie shop assistants, who would steal banknotes from the cashier...

To have sticky fingers means to steal.

Also, the bureaucratic pun doesn't work, because slow bureaucrats actually keep their jobs...

I actually lived in the US quite a while, went to school there, and never encountered the the noun 'clerk' in relation with salesmanship. The word 'clerk' is rarely used in the US at all. I don't believe employee is a precise enough translation of 'clerk'. Isn't there a better French word for it?

Then you missed something back there. It's a big country...

http://en.wikipedia.org/wiki/Clerks

http://www.rottentomatoes.com/m/clerks/

I had missed a lot, although I don't miss it at all.
The question is, are 'employees' not too general for this context.

I already replied :

Out of context, these "clerks" can be either standard office employees (British English) or shop assistants (US English, as I just demonstrated in my reference above).

For both cases, we use « employé » in France.

We might specify « employés de bureau » if we know for sure they're office ones or « employé de/du magasin » if they are shop assistants, but we wouldn't bother to specify in such a general consideration where the context is implicit.
Here, I think it applies to shop assistants who steal from the cashier, but you're free to imagine other contexts...

You must not be annoyed because translations diverge from the context you have in mind, if it applies. it is normal. The [epo] sentence translates this French sentence and it is normal that it diverges from English as languages don't match one to one and different contexts can be extrapolated. You are free to coin yet other esperanto translations from the English sentence, with no effect on this French sentence...