Could I have caused a problem with the hot water solenoid with my thermostat installation? (Furnace seems to function correctly, except for my concern that fan only temps are sometimes a little warm.)

And, if the solenoid is stuck in open, or partly open, is this a minor problem that can be safely ignored if room temperatures are comfortable?

After installing a digital thermostat on our condo unit (which connects to a central boiler/ac unit for the building) I checked furnace outflow and the air seems a bit warm for when I only have the fan turned on. And when the heat is On, the air temp varies a lot at different times, I assume because the central boiler is set for different temperatures during the day/night cycle. So it's frustrating to check because often the heating temperature isn't very hot and easy to distinguish from the fan cycle.

It could be many different things.

As you said zone valve/solenoid Valve leaking.
Wrong thermostat (some systems use a special thermostat on hot water fan coil systems).

In some systems running the fan when there is no call for heat can add more hot air into the rooms. This is caused if they used a zone valve intentionally design to bleed a bit of hot water all the time as to prevent freezing of the lines when not occupied.

I do not know the exact system you have or it components since they were not supplied with the question. If it is working OK then leave it alone. If the temps are getting to high over the setting try turning the blower to auto instead of on.