Are leaderboards broken?

Well, first make sure this is a server script inside of Workspace or ServerScriptService.

Second, make sure it's not disabled.

I've always used IntValues for the leaderstats object, but since the wiki says Models are fine I'll assume that's true.

Add print()'s to your script to try to find where the problem is.

In the past, PlayerAdded events have not fired in PlaySolo. I thought Roblox fixed this, but try starting a server and seeing what happens.

When testing in Solo, the player usually arrives before Scripts start running.

This means when you get to the PlayerAdded connection, it's too late for you to capture the first player joining.

The simplest way to fix this is something along the following:

function newPlayer(player)
    local leaderstats = Instance.new("IntValue", player)
    leaderstats.Name = "leaderstats"
    local money = Instance.new("IntValue", leaderstats) 
    money.Name = "Money" 
    money.Value = 0
end

game.Players.PlayerAdded:connect( newPlayer )
-- For all future players, use the event

-- For all the players already joined, let's just *say* they joined
-- just now:
for _, player in pairs(game.Players:GetPlayers() ) do
    newPlayer( player )
end

Note that the IntValue for leaderstats is the canonically correct instance (not Model), though I'm unsure whether or not other types of classes will work.