Build System Flying Towards Camera?

The problem is that the ray from the mouse is hitting the object you're trying to build, thus moving it slightly closer to the camera each tick.

To bypass this you can use Mouse.TargetFilter, which determines what objects should be ignored when casting the ray.

Here's the syntax and context of the code:

Mouse.TargetFilter = workspace.Baseplate -- now the mouse ray will ignore the baseplate object

And here's your script but with the implementation:

local mouse = game.Players.LocalPlayer:GetMouse()
local Model = workspace:WaitForChild('Window1')

local posX = mouse.Hit.X
local posY = mouse.Hit.Y
local posZ = mouse.Hit.Z

local function Snap()
    posX = math.floor(mouse.Hit.X)
    posY = mouse.Hit.Y
    posZ = math.floor(mouse.Hit.Z)
end

mouse.Move:Connect(function()
    Snap()
    Model:SetPrimaryPartCFrame(CFrame.new(posX, posY + 3.7, posZ))
end)

local function Place()
    local WindowCopy = game:GetService('ReplicatedStorage').Objects.Window1:Clone()
    WindowCopy.Parent = workspace
    WindowCopy:SetPrimaryPartCFrame(CFrame.new(posX, posY + 3.7, posZ))
    mouse.TargetFilter = WindowCopy -- Now the mouse's raycast will ignore the window
end

mouse.Button1Down:Connect(function()
    Place()
end)