The idea was to build an easily expandable, yet fully automatic farm that can be relatively easily rebuilt and delivers a steady flow of items instead of a huge load every few hours. The biggest problem was to find a suited clock mechanism for this.

So here's what I came up with:


The Spawning Area

It uses a diagonal order of rows, so that half of them can be used for seeding mushrooms which spawns more mushrooms onto the other half of the rows. Each of these are surrounded by 4 seeding rows and can be flushed with redstone (using a piston which is placed on one of the seeding rows next to it).

Redstone

I found a viable solution for the above mentioned problem using cacti. One cactus serves 2 pressure plates (each of which activate the water flow on one column) meaning it may drop cactus blocks on one of them each time it tries to grow. Unfortunately, the item will stay there for 5 minutes preventing more mushrooms from spawning. So it's nowhere perfect, but does the job and is relatively easy to build.

A lever can be added to disable automatic farming entirely (allowing more mushrooms to grow in that time).
For manual farming with a button you need a monostable circuit to expand the pulse long enough for the water to transport the items all the way to the end of the stream. I found an efficient design by MinecraftAddict for this.

Efficiency

According to some quick tests, one row on one side yields about 1.75-2.0 mushrooms/hour.
Son if you wanted your farm to fill your inventory over a period of 10 hours (230 items/hr) you could make it 8x8 rows on both sides (like shown) using 2 stacks of pistons.

Manual harvesting per button is far more efficient though (if you wait long enough), so you can both use it to farm while being idle as well as pushing the button every now and then while doing stuff around your base.

But efficiency wasn't my initial goal, because since you can expand/repeat it, you can make it almost as big as you want to increase efficiency.