From: John Doty (jpd@space.mit.edu)
Date: August, 1995
Original source: Usenet's rec.radio.amateur.antenna

Statement: You can live with large losses in a medium wave receiving antenna because signal and noise levels are very high...

Would this mean that it in everyday, normal life is quite okay to connect a 50 ohm coax to that long stretch of copper wire - and simply forget all about those baluns?

Well, first forget the term "balun" and substitute "matching transformer". A balun is a special type of transformer that performs better than a conventional transformer in certain specialized circumstances. Conventional transformers work fine for receiving below a few hundred MHz. Conventional transformers are simpler to construct (just a primary and secondary winding) and offer a wider variety of transformation ratios.
Baluns are an amateur radio affectation that's misplaced in shortwave (or longer) listening. The transmission of power at HF is one of the specialized applications where baluns are appropriate, but reception isn't.

My beverage antenna is running right under a local power line (low power) in approx. 90 degrees. This works fairly well when the weather is dry, with slight interference. Things tend to change when rain, mist and snow sets in. Somehow the wire is electrified, and occasionally (mostly in foggy and snowy weather conditons) even sends out pretty uncomfortable sparks. I suppose a coax from my QTH to well beyond the other side of the power line (approx. 100 meter) could solve that problem.

Sounds like an excellent application for coax. Be sure you ground the shield both at the base of the antenna itself and near your house. Burying the coax will help.
The sparks are probably not due to the power line, but rather normal "precipitation static". For a large antenna it is highly desirable to bleed this static off. A matching transformer with DC continuity to ground will do this, or you can use a resistor to ground: a few thousand ohms is a good value.

Would I have to correct any mismatch when using a coax, or would it be better to ignore the balun totally (in spite of any mismatch)?

An obsession with matching is another amateur radio affectation that's misapplied to reception. Matching is always important if you're transmitting, but it's less important for reception. The longer the wire, the less you need to worry about matching. The lower the frequency, the less you have to worry about matching. At microwave frequencies matching is almost always important. A coax-fed 6.5 meter wire antenna will be seriously deaf in the 13 meter band without some sort of matching device, but in other shortwave bands the mismatch won't be a serious problem with an adequately sensitive receiver. A Beverage antenna at mediumwave should be extremely tolerant of mismatch unless your receiver is unusually insensitive.
It's easy to tell when you have an adequate match: if the noise level in your receiver increases when you attach the antenna then the match is good enough. In this case, any improvement in signal transfer from antenna to receiver will increase signal and noise by equal factors, so no improvement in signal to noise ratio will be achieved by using a better match.