The errors in T and 𝓁 come from your measurement, and you have to judge how big they are. e.g. I would guess timings are only accurate to about ¹⁄₂ a second and lengths to about a millimetre.
So it's a bit misleading to say ψ² tells us the probability of the electron being at that position. It's more like telling us how much of the electron is at that position.