[Solved]How would I get a previous mouse target when the mouse changes targets?

The short answer is to assign the current target to a previous target variable at the end of the function (but only if the current target is different from the previous target).

You should keep code that you only want to run once outside of event code. For instance, you only need to check if the player has ObjTarget once. You should never set up an event within another event, as you do with objTarg.Changed.

--I assume you have a variety of variables defined here

--Create objTarget if needed
local objTarget = plr:FindFirstChild("ObjTarget")
if not objTarget then
    objTarg = Instance.new("ObjectValue")
    objTarg.Value = nil
    objTarg.Name = "ObjTarget"
    objTarg.Parent = plr
end
local previousTarget

function IsValidTarget(target) -- returns true if the player can target the specified 'target' object
    for i, v in ipairs(tycoon) do
        if v == target then return true end
    end
    return false
end

mouse.Move:Connect(function()
    if not placing then return end -- do nothing if not placing something
    local mseX = mouse.Hit.X
    local mseY = mouse.Hit.Y
    local mseTarget = mouse.Target

    if mseTarget and IsValidTarget(target) then
        -- Update objTarget
        objTarg.Value = mseTarget
        -- Update previousTarget
        if mseTarget ~= previousTarget then -- if they are the same then the user has simply moved the mouse a bit and hasn't changed targets, so only update previousTarget if they are different
            previousTarget = mseTarget
        end
    end
end)
-- TODO: When you set 'placing = true', you probably want to do "previousTarget = nil", too (if not, be sure that 'previousTarget' is set to nil somewhere)

If you need to access previousTarget outside this script, you'll need to turn it into an ObjectValue just like ObjTarget.