There are a lot of disadvantages when it comes to keeping octopi. The first being their longevity (or lack of). Many species will not live over a year. I think average lifespan is from one and a half to two years. They can not safely have any other tankmates. They are also Extremely intellegent and curious. If they are able to remove the lid from a jar, You can imagine how easy it would be for them to find a way out of even a well secured aquarium hood. Escape is a big problem with octopi. if an opening is large enough for their beak to fit through, than so can the rest of the octopus. (an octopus with a 6 foot armspan can fit through a hole the size of a quarter.
You might have heard about the octopus at I believe some fish store. Expensive fish kept dissapearing from tanks near the octopus' tank, (eventually from tanks across the hall, farther away from it's tank). They thought that an employee was stealing the fish, so they set up video cameras to catch who was doing it. What they did catch on tape, was the octopus leaving his tank, moving across the floor and into other tanks, eating the inhabitants, and returning to his own aquarium. Pretty amazing huh?
Just some things to consider before bringing home an octopus.
Also, their requirements (temperature and the like) will very greatly between species, so be sure to do your homework, and know which species you will be acquiring before setting up an enclosure.