Why would cold water run from the hot water faucet (for about a minute), after the hot water was already flowing? This happened in two washrooms, at different sides of the house, but not at any other faucet. Hot water then flows normally. This does not seem like a problem with a diverter, filter, hoses too close together or any of the other solutions proposed in related threads. Any suggestions?
Water cools at different rates in different parts of the system
Basically, the pipes from the heater to the faucet are not in the same thermal conditions.
For example, pipes in internal walls are at indoor air temperature (say 20C) and pipes in roofspaces will be at (close to) outside air temperature (say 5C to 40C depending on where you live). If the pipes are full of hot water (say 70C) as they are after being used, all else being equal, the greater the temperature gradient, the quicker they cool.
Add to this that the thermal insulation between the pipes and their surroundings will not be uniform and its not unusual to get a part of the system that retains heat for longer than other parts. If you turn on the taps shortly after they have been used you will get "bubbles" of cold being pushed along.