Acceptable level of hum at max volume?

True hum, by the classical definition, is 60Hz OR 120Hz noise generated by unrectified AC voltage getting in to the signal path or by improper or inadequate grounding. The frequency would depend on the configuration of the rectifiers in your power supply. Since tubes and transistors are capable of amplifying those frequencies with equal efficiency, I see no reason why "hum" would be associated with tube equipment vs solid state. If this is what you are hearing, and if it bothers you, you could ask a technician to improve the rectification in your power supply or check the ground scheme, to reduce the hum. Any experienced tech or DIY guy would have some ideas of what to do. But as to what you are complaining about, I would do nothing.

Actually, I may have overlooked one factor that does differentiate tubes from transistors, and that is with regard to the filament supply. I suppose it is possible, even in an indirectly heated triode, that noise in the filament supply could leak into the cathode, and the AC component might then be amplified as hum. In a well designed tube preamplifier or amplifier input stage, the filament voltage should be fully rectified to DC, with very low AC component, and regulated. If the filament supply circuit is malfunctioning or if there is a "leak" between filament and cathode within a given tube, the result might be a faint hum. In either case, repair is possible. (If the source is a filament to cathode voltage leak, the tube should be discarded and replaced. Perhaps that is what Jburidan experienced.) A competent tech should be able to figure that out.