I've played the Firefighter career three times so far, three different Sims, three different towns, and this last one after uninstalling the game from my laptop entirely, and then reinstalling and starting fresh; and in none of them have I been able to find the fire extinguisher. My firefighters are currently at level 1, level 6 and level 10.
I have maintained and upgraded the fire alarm (and goodness, those are all over the building, aren't they?) and I have maintained the upgraded the horsepower on the fire engine to level 3 (which does not show up in the Skill Journal for handiness, but oh well), but I absolutely have not been able to locate a fire extinguisher.
It is not in my personal inventory (what my kids and I call "in my pocket") and it's not in the family inventory.
If it helps, I have all expansions and 'stuff' packs. If this helps also, my other major glitches are: 1) I completed the Criminal career as Master Thief and did NOT get a golden fox statue (I have not yet tried Emperor of Evil to see if I get the red aura), and 2) I have the China-lag problem, which I have read about elsewhere. On the other hand, I completed the Culinary Career and I did get the Kelvin Minus-1 fridge. Also, if it helps, I don't use cheats or mods.
By the way, this is my first post. Thanks so much for any help! I want to do 100% of the upgrades for the Handiness trait and it's driving me crazy!