Nick
In your original post you referred to a Bzzz from the tweeter, rather than a hum which would be much lower in frequency, which is why I am persuing the possibility of an intermittent high frequency oscillation. Due to intermodulation effects, a high frequency oscillation can cause noise within the audible frequency range.
If however you are experiencing a definite hum (50 or 100Hz UK, 60 or 120Hz US etc) then you need to look elsewhere. Being intermittent, I would suggest a dry joint or faulty resistor/capacitor. In the absence of further information on this, I will proceed with the assumption of a hf oscillation.
Answering/confirming your queries/comments:
Keeping the output transistor leads close together prevents the formation of a loop which could cause oscillation.
The Zobel network provides an increasing impedance to the output stage as the frequency rises which improves amplifier stability particularly into inductive loads. It is indeed as shown in Project 3A.
You are correct about the base resistor. It is connected in series with the lead to the base, at the transistor end of the lead. Its purpose is the same as the gate resistor in MOSFET circuits, to reduce the possibility of oscillation in the output devices (as opposed to Nyquist oscillation of the whole circuit). MOSFETs need this resistor as they have a very high ft. Some BJTs require it for the same reason or to overcome defective layout or wiring. The MJ15003 should not need a base resistor since it doesn't have a high ft. However, if the base resistor cures the problem, it indicates that either the transistors are out of spec or the laout/wiring needs some alteration.
100nF decoupling caps. I use polypropylene, ceramic are best from the point of view of impedance. Use whatever you have available (anything between 50nF and 500nF) just to provide a lower impedance path to earth at higher frequencies.
Yes, the 4k7/330pF form a low pass filter at the input (-3dB at about 100kHz) which reduces the amount of rf entering the amp.
Again yes, the 100pf cap creates a dominant pole which causes the high frequency gain of the amp to roll-off earlier, increasing the Nyquist stability. If this cap cures the problem, it again indicates that you have a component or layout fault.
The quiescent current can be increased to 3-4A but you will need additional output transistors, some 0R1 emitter resistors and higher wattage resistors in the bootstrap circuit. See the 'JHL for ESL57' article on my website for details. Note, if you decide to do this, the optimum supply rail voltage and quiescent current will depend on the impedance of your speakers.
Geoff