You need it when you are recovering the Mech Motor and Living Quarters key from the Greenhouse in the Production zone (far right of the island). When you take the key from the robot janitor, you set off an alarm that prevents you from leaving the way you came in. Climb to the roof dome and use the mallet to break open the dome.
*You will also need the Dirty Beaker from the Museum before you go to the research lab in the production zone. You need it to reach the closet for the key.
When you are getting the Living Quarters key from the closet in the Greenhouse of the research lab (production zone), you set off an alarm. Since you cannot leave the way you came, use the rubber mallet to break the glass dome near the upper left corner of the lab.
There is one part of the island where you use it to break glass to make an escape route because the entrance you originally came through you can't get back out of because of a thing that fires water at you. Hope this helped! :)
If you are talking about skullduggery you use it to hit the gong to scare the fish. If you are talking about steamworks you use it to get out of the greenhouse
You don't. You have to go up to the dome, to the far left and use the mallet on the crack to break the glass. --- Once you use the herbicide and reach the Maintenance Closet, taking the Living Quarters key sets off the alarm, so you cannot go out the way you came it. Hopefully you have the Rubber Mallet from the junk bin at Sully's. If not, return the key to the robot, leave, and come back with the mallet. Once you have the key, climb up the the top of the dome, and you will find the glass is cracked and weak on the left side. Use your mallet to smash the glass, and exit.
When you are in the Greenhouse (research lab aka production zone), you can use a herbicide to reach the closet with the Living Quarters key. However, taking the key sets off an alarm, and a fire hose prevents you from leaving the way you came in. Instead, climb to the ceiling and go to the upper left inside the glass dome. The glass is cracked there and you can use the Rubber mallet to break it and escape. (If you don't have the mallet, replace the key to shut off the alarm, then go get the mallet from the trash at Sully's and come back for the key.)
use the crab.
You need the key, which is in a closet in the lab in the Production Zone (far right). Get the mallet from Sully's and the beaker from the museum before you go there. (see the related question)
The island opened to general use on September 9, 2010, concurrent with a new island map. Steamworks Island will normally be in the center or bottom center of the map.
You use it when the time comes. In the Production Zone (far right, across the Drawbridge) you recover the Steam Motor and the key to the Living Quarters. To escape, you climb up and smash the glass dome with the mallet. You will also need the dirty beaker from the upper right inside the Museum.
Use it for the steam terminals
You should already have the robot crab from when you got Sully's key. You also need a length of vine that is atop the building to the left of the Living Quarters. Go right to the Hub at the right of Main Street. Use Sprocket to drop the robot crab on the "hot hatch" to cool it off, so you can enter the underground.
You go to the upper left cornet and use the rubber mallet (this is at sully's place where the mech is too) to break the glass, this is how you get out... If you don't have the rubber mallet yet, bring back the key and go get the mallet