The article makes a distinction between Aurors and people who work for the Ministry of Magic but the Aurors do work for the Ministry. Since Cracked makes that distinction then I will as well. Here is a quick list of the different departments in the Ministry of Magic from HP Lexicon:
Department of Magical Law Enforcement
- Improper Use of Magic Office
- Magical Law Enforcement Squad
- Misuse of Muggle Artifacts Office
- Office for the Detection and Confiscation of
Counterfeit Defensive Spells and Protective Objects
- Wizengamot and Wizengamot Administration Services
- Council of Magical Law
- Magical Equipment Control
Department of Magical Games and Sports
Here you'll find not only the British and Irish Quidditch League Headquarters but also the Official Gobstones Club and the Ludicrous Patents Office.
Department of Magical Accidents and Catastrophes
The Department operates teams which can respond at a moment's notice to a magical accident. These teams include:
- Accidental Magic Reversal Squad
Also referred to as the Accidental Magic Reversal Department in earlier editions of the book, this team is the first on the scene when a magical accident or catastrophe occurs. The team will include trained Obliviators to modify memories of Muggles on the scene.
Although not specifically stated as being in this department, it seems logical, since this group casts various forms of invisibility magic to hide magical places and creatures from Muggle eyes (DP).
- Muggle-Worthy Excuse Committee
This group is responsible for creating alibis and providing alternative (non-magical) explanations for magical accidents to pass along to the Muggles.
Department of International Magical Cooperation
The dept. duties include:
working with magical governments of other countries
setting standards for trade
creating regulations for things like cauldron thickness
worked with Department of Magical Games and Sports on the Triwizard Tournament
They also work with the
International Confederation of Wizards, British Seats
International Magical Office of Law
International Magical Trading Standards Body
Department of Magical Transportation
- Apparition Test Center
- Broom Regulatory Control
- Floo Regulation Panel/Floo Network Authority
- Portkey Office
Department for the Regulation and Control of Magical Creatures
- Office of Misinformation: Beast Division
- Centaur Liaison Office
- Committee for the Disposal of Dangerous Creatures
- Dragon Research and Restraint Bureau
- Pest Advisory Board
- Werewolf Capture Unit
- Werewolf Registry
- Being Division
- Goblin Liason Office
- Office of House-Elf Relocation
- Werewolf Support Services
- Spirit Division
Department of Mysteries
Committee On Experimental Charms
If you add in all of the support staff that any bureaucracy needs you have a lot of jobs.
If we add in Kevin's answer we have a lot of different jobs.