Alright, actual pros: HUGE power spike at 6. Reset champ. Good escape (since W gives vision). High burst (duh, assassin). Very mobile.
Cons: While relatively easy to learn the basics of, Akali is actually pretty difficult to master. CC pwns her hard. If she ISN'T snowballing, she won't snowball due to item dependency. Weak laning pre-6. Highly squishy. Is beaten by trinket items.
She's one of the 'freelo' champs. I realy hate that word, but it's true. She's powerful in silver and bronze, but once you start getting into the level where people are counterpicking, she has SO MANY hard counters that it's relatively easy. People don't really know how to respond to her in lower levels. Example: Annie. While normally an easily counterable champ, Akali doesn't really stand a chance. Annie gets her stun up, then just nukes Akali into oblivion. Akali is forced to build MR just to survive in lane, and is not getting her snowball effect or her items that she REALLY needs to do well.
Learning how to counter champs like Akali, Yi, and WW are key to getting better at the game. While VERY powerful at lower levels of play, they have tons of counterplay. Learning how to counterplay is how you get better at the game. Notably, I am imperfect at this as well - hence being silver.