1. Low primary DC resistance for little insertion loss
2. High permeability alloy lamination core material
3. Static shield between windings to reduce capacitive leaking
4. Relatively small core size, usually less than a square inch
5. Mu shield encasing in many cases to reduce external magnetic fields.
Since a mike amplifier often has a very high input impedance, #1 isn't really about "insertion loss". In a big power transformer we want DCR around 2% of nominal impedance to reduce power loss, but in a typical mike transformer application even DCR as high as 50% of nominal impedance won't reduce output much.
50% DCR will however raise noise resistance to about 2dB Noise Figure. So we can be a little relaxed, but not careless.
#1 and #2 go together. For a given size, permeability and bass response, you need a certain number of turns. For a higher permeability, you can do it with less turns of fatter wire, reducing DCR automatically. Actually the key spec for high impedance windings is leakage inductance, which increases with number of turns; a hi-perm core extends the range between bass fall-off and trouble in the treble. With Permalloy you may get low DCR without trying. However Permalloy is expensive, so you tend to reduce core size and cost (hence #3), and DCR comes back up.
It is not an easy optimization.
#5: The mike transformer is generally the lowest level in the whole system. And systems have volts of signal and hundreds-volts of power laying around. So crap gets in the mike transformer. Distance is the cheapest shielding, and usually enough isolation for line transformers. Mike transformers very often need magnetic shielding.
#3: In an ideal transformer, we turn electric energy into magnetic energy, and turn that back into electric energy. The two sides of the transformer may be at very different voltage potentials, but that won't couple across the magnetic path. But to get good magnetic coupling, the two windings have to be very close together. That adds little capacitors from one winding to the other. Now any voltage potential on one winding will couple to the other, and usually in unexpected ways. If you foolishly wind a simple primary over secondary winding, and foolishly connect the outside of the secondary to the grid of the amp, at high frequencies all the common-mode voltage on the primary couples right into the grid. In this case, reversing the connections on the secondary couples the capacitive crap into the grounded side of the secondary, while the grid sees only the crap on the core which can be grounded and quiet. It gets more complicated when, to reduce leakage inductance, you interwind P-S-P-S-P so more of the primary inductance drives the secondary and grid (low leakage inductance); now you have capacitors all over and there is no way to phase them to avoid capacitive leakage into the grid. You can put electrostatic shields between windings, but that may raise total capacitance and lower the upper resonant frequency.
And mostly, low-impedance transformers like 150:1,000 don't have huge problems. They only need around a thousand turns, so insulation doesn't take up a lot of space like when you have many-thousand turns (you can make copper smaller, but there is a minimum thickness of varnish to avoid shorts). You can easily give them a hi-Z load so the leakage inductance is not too bad for treble. The capacitance is proportional to overall size, not number of turns, and may be 300pFd; this is "small" compared to 1,000 ohms but large next to 50K ohms. Yes Deane and crew worked hard on a "simple" 200:800 design, wringing every last bit of performance. But very simple techniques can give very-good performance at low impedance. Things get much harder over 10K nominal impedance, so much that compromises must be picked.
> What sort of winding techiques are used in these transformers? (reverse winding, alternate winding, random winding, etc.)
Depends mostly on the impedance. If you don't need extreme bandwidth, at low Z you can throw them on any old way. At high impedance, you may have to tediously compute several alternate winding techniques, and then compromise with what your winding machine can really do well.