Script Only works in Edit mode and not When I publish the game?

Hey, I have figured it out for you. First, the LocalScript should be in StarterGui. The trail can't be in the ServerStorage if you want to clone it locally. So you need to put the trail in the Workspace. I have improved your script a bit because it gave me some errors. here's the script:

--Getting the Camera
game.Players.PlayerAdded:connect(function(player)
    script.LocalScript:clone().Parent = player.CharacterAdded:wait()
end)    


--Local Variables   
local cam = workspace.CurrentCamera
local player = game.Players.LocalPlayer
game.Workspace:WaitForChild(player.Name)
local Char = player.Character
local Humanoid = Char:WaitForChild("Humanoid")
local Mouse = player:GetMouse()
local lastTapTime = 0
local clicked = false
local Trail = game.Workspace.Trail:Clone() --I have changed it to Workspace because you can't get anything from the ServerStorage locally.
_G.Energy = 100
local Mouse = player:GetMouse()



--Moving the Humanoid
    --Double Tap
enabled = true
Mouse.KeyDown:connect(function(key)
    if not enabled and clicked then
        return
    end
    if key == "w" and _G.Energy >= 25 then
    enabled = false

    local function onTap()
        if tick() - lastTapTime < 0.2 then
            print("double Click!")
            clicked = true
                --What happends when the user double taps
            player.Character.UpperTorso.Velocity = cam.CFrame.lookVector * Vector3.new(1,0,1) * 400
            Trail.Parent = Char.HumanoidRootPart
            local attachment0 = Instance.new("Attachment", Char.Head)
            attachment0.Name = "TrailAttachment0"
            local attachment1 = Instance.new("Attachment", Char.HumanoidRootPart)
            attachment1.Name = "TrailAttachment1"
            Trail.Attachment0 = attachment0
            Trail.Attachment1 = attachment1
            wait(0.3)
            Trail:Remove()
            _G.Energy = _G.Energy - 25
            wait(0.5)   
            end
        end

        onTap()
        lastTapTime = tick()

        wait(0.5)
        enabled = true
        clicked = false
    end
end)

--Double Jump
enabled = true
Mouse.KeyDown:connect(function(key)
    if not enabled and clicked then
        return
    end
    if key == " " and _G.Energy >= 12.5 then
    enabled = false

    local function onTap()
        if tick() - lastTapTime < 0.2 then
            print("double Click!")
            clicked = true
                --What happends when the user double taps
            player.Character.UpperTorso.Velocity = Vector3.new(0, 100, 0)
            Trail.Parent = Char.HumanoidRootPart
            local attachment0 = Instance.new("Attachment", Char.Head)
            attachment0.Name = "TrailAttachment0"
            local attachment1 = Instance.new("Attachment", Char.HumanoidRootPart)
            attachment1.Name = "TrailAttachment1"
            Trail.Attachment0 = attachment0
            Trail.Attachment1 = attachment1
            wait(0.3)
            Trail:Remove()
            _G.Energy = _G.Energy - 12.5
            wait(1)   
            end
        end

        onTap()
        lastTapTime = tick()

        wait(0.5)
        enabled = true
        clicked = false
    end
end)

--Repleneshing Energy
for i = 1, math.huge do
    wait(0.1)
    print(_G.Energy)
    if _G.Energy < 100 then
        _G.Energy = _G.Energy + 12.5
        print(_G.Energy)
        wait(2)
    end
end

If you have any other questions or issues, please tell me.