Based on a Naaleh.com shiur by Rabbi Shimon Isaacson
One should not tie the drawstrings of a garbage bag together in a bow knot as it is meant to last. A single slip knot is permitted.
Knots that are prohibited to be made on Shabbat may not be untied on Shabbat. Therefore, one may not untie a permanent knot, such as a tzizit knot, on Shabbat.
One may untie an inadvertent knot that was formed while undoing shoelaces.
One may not undo the knot on a bakery box as it is considered permanent. It should be cut open instead.