Peter,

Some DIY sources suggest embedding a wire mesh in the mortar bed
shower pan. What is the purpose??

I believe it's reinforcement to help keep the mortar bed from cracking. If
it does crack, the wire holds everything together.

I built a large 6'x6' curbless shower. I could not find the recommended
wire lath locally, so I used galvanized 1/4" hardware cloth. It worked
fine.

The wire mesh goes over a layer of plastic. This partially protects the
subfloor below from the moisture of the mud bed and may act as a bit of an
isolation membrane. More importantly, it keeps the plywood subfloor from
"sucking" the moisture out of the mud bed before it can set up properly.

I used a waterproofing membrane called "Schulter Kerdi" and their
proprietary drain system. Unlike the vinyl liner method, this keeps the
water out of the mud bed in the first place instead of trying to deal with
water that seeps through the mud. It also means you only need to make a
single mud bed instead of two. It's a great system, and I highly recommend
it.

You can find a lot of examples and helpful advice on the John Bridge tiling
forums at www.johnbridge.com.

Take care,

Anthony