While the second part is wrong, the Fourth Mizukage was brainwashed by an Akatsuki member. During the Kage Summit, the Raikage accuses Kirigakure of harboring Akatsuki activities and suspects that the organization had its origins there. There was the infamous Academy graduation method, questionable loyalty of many of its ninja (Kiri has the most number of missing-nin, including all of its Swordsmen of the Mist), and the deplorable persecution of ninja with kekkei genkai.

Token Evil Teammate: Kirigakure has the worst reputation among the hidden ninja villages and this is not without merit.

Zabuza got the badass reputation and his supposed fog-based abilities as well as his Water dragon (which here is just another Water jutsu), while Haku got the feminine appearance and cross-dressing.

Public Domain Character: Zabuza and Haku are based on Kirigakure no Saizo (Saizo of the Hidden Mist), a legendary ninja who also lends his nickname to the Hidden Mist Village.

More Teeth than the Osmond Family: Particularly, the seven swordsmen and potential members.

Making a Splash: The village specializes in water jutsus.

Hufflepuff House: While its ninja have been appearing since the very first arc of the series, Kirigakure as a village doesn't play a role until the Five Kage Summit arc.

Hoist by His Own Petard: The horrible training regimen they implemented only served to weaken their village rather than strengthen it, as well as creating a host of psychotic ninjas.

In recent years, the Hidden Mist has tried to distance itself from its horrific reputation. The village quickly discontinued this after a young Zabuza murdered 100 students during the exam.

Everybody Has Standards: The village was infamous for its brutal training including a final exam where aspiring ninja would kill their classmates to prove their worth.

If you had kekkei genkai, then your life simply sucked. If you want to become a ninja, you had to kill a fellow student just to graduate from the class.

Crapsack World: During the Bloody Mist era.

Hidden Mist Village provides examples of:

Village hidden in rain