Part Rotates After Placing?

You have the right idea, but you're not using the disconnect function correctly. You need to define a variable for the event connection. This way, you can use the disconnect function on that connection variable.

local player = game.Players.LocalPlayer
local mouse = player:GetMouse()
local blankPart = game.ServerStorage:WaitForChild('WoodWall')

script.Parent.MouseButton1Down:connect(function()
    if player.leaderstats.Wood.Value >= 5 then
        player.leaderstats.Wood.Value = player.leaderstats.Wood.Value - 5
        script.Parent.Parent.Parent.Parent.Visible = false
        local part = blankPart:Clone() 
        mouse.TargetFilter = part
        local moveConn = mouse.Move:connect(function()
            local p = mouse.Hit.p
            part.Position = Vector3.new(math.floor(p.X),math.ceil(p.Y),math.floor(p.Z))
            --Assign event a connection variable
            keys = mouse.KeyDown:connect(function(key)
                if (key == "r") then
                    part.CFrame = part.CFrame*CFrame.Angles(0,math.pi/2,0)
                end
            end)
        end)
        mouse.Button1Down:wait() 
        moveConn:disconnect() 
        keys:disconnect(); --disconnect from connection variable
    end
end)