Well, paying a bit more attention to the technicalities of ice hockey (like trying to figure out what in the world is the difference between icing and off-sides), I discovered what one is supposed to do with the octopi thrown in the Joe Louis Arena, a fact which no one had ever been able to answer. But, of course, these days there is the omnipotent god Wikipedia:
The 1952 playoffs featured the start of the tradition—the octopus throw. The owner of a local fish market ... threw one from the stands onto the ice. The eight legs were purportedly symbolic of the eight wins it took to win the Stanley Cup at the time. The Red Wings went on to sweep both of their opponents that year en route to a Stanley Cup championship. The NHL has, at various times, tried to eliminate this tradition but it continues to this day. ... since [arena] does not condone the throwing of any foreign objects onto the ice, fans often sneak the sea creatures in wrapped around their bellies in trash bags. The boiling process also lessens the odor and allows the fans to get past security.
There is a certain etiquette that must be followed for fans that wish to throw octopuses onto the ice.
Beforehand, an octopus should be boiled for at least 20 minutes on high heat with a little lemon juice and white wine. This will mask the creature's odor as well as reducing the amount of slime. A raw dead thrown octopus would result in a smelly ball that would stick to the ice upon impact and possibly leave an inky stain, while a well-boiled octopus will bounce and roll across the surface of the ice.
After the octopus has been properly prepared it must be smuggled into the ice arena, as it is against the law in Detroit (and other NHL cities) for a fan to throw anything onto the ice during a game. A preferred method is to wrap the octopus in plastic (a trash bag or a large Ziploc bag will do) and then wrap the package around one's middle section to give the appearance of a beer belly.
The most appropriate time to throw an octopus onto the ice is after the national anthem is sung or after the Red Wings have scored a goal. The octopus must be thrown onto the ice surface in an area that is clear of all players. It is never acceptable to aim for opposing players. Tactics are also used to protect the identity of octopus-throwers from arena security. It is common practice for the hurler to ask the surrounding people to stand up with him to shroud the task in anonymity.
Experienced throwers grasp the octopus around the middle of its arms with the octopus's head (or more correctly, its mantle) hanging down near the thrower's knee and then swings the octopus with an overarm motion. Holding the octopus by the ends of its arms prior to the throw may result in the mantle of the octopus breaking off during the wind-up.
After successfully participating in this peculiar tradition, the octopus thrower is left with a tell-tale indicator: stinky hands. It is advisable to bring along a wet wipe and a slice of lemon to assist in removing the odor.... the Joe Louis Arena head ice manager and one of the two Zamboni drivers, is the person who retrieves the thrown octopi from the ice. After he retrieves an octopus, he has been known to twirl it above his head as he walks across the ice rink to the Zamboni entrance.
... sent a memo to the Detroit Red Wings organization that forbids Zamboni drivers from cleaning up any octopuses thrown onto the ice and imposes a $10,000 fine for violating the mandate. The linesmen will instead perform any clean-up duties. ... justified the ban because "matter flies off the octopus and gets on the ice" when ... it [is swung] above his head ... Detroit Free Press dubbed the prohibition as "Octopus-gate". By the beginning of the third round of the 2008 playoffs the NHL loosened the ban to allow for the octopus twirling to take place at the Zamboni entrance.