Credit for finding this bug goes to Emanuel Armasoiu (testing on Samsung Galaxy Mini 2 Android 2.3.6)
I confirmed on Samsung Galaxy S4 Android 5.0.1 MCPE 0.12.3 single player. All methods below work in survival and creative.
what happened:
First method
place a boat near to the wall that you want to walk through so that the boat is partially in the wall (see the image original find.png)
Board the boat
Leave the boat (or you can destroy it)
Walk directly into and through the wall
If you walk through quickly, you take little or no damage in survival.
Second Method (images 1-5 creative, 6 in survival)
place a boat so that part of it is inside the wall
Board the boat and press both arrows at the same time until you "paddle" through the wall
Leave the boat (or you can destroy it)
I expected boarding a boat that is partially through the wall would not let you pass through the wall. Alternatively, I expected that placing a boat partially in a wall would "bounce" the boat out of the wall or would not let you board the boat.
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Update, this only works for passing through one block. You will be stopped by the next solid block horizontally in any direction.

Cannot Confirm on Samsung Galaxy Note 5. Android 5.1.1 Version: 0.13.0 Build 5

What?! cannot repro... /AFK ... /runs to boat...

I'm back. And yes, I just passed through a wall in a boat on 0.13 build 5. 😛

Reconfirmed on 0.13.0 alpha
Devices
Samsung Galaxy Note3
Android 5.0
and
Samsung Galaxy Tab 3
Android 4.4.2

I can also push a boat through the wall.
-Make a fence or stone wall.
-Place the boat by the wall so it goes through a little.
-When you push the boat it will come out the other side of the wall.

Reconfirmed this in 0.14.1

A bit harder to do in 0.15.2 but I can still do it in creative single player.

Cannot reproduce the issue as of 0.16.0 build 1. Assuming it's been fixed.

I can reproduce this in 1.14.60. It is easiest going west, a little harder north and south, and not reproducible going east. In most cases (depending on direction and exactly where you point the cursor) there needs to be air under the wall/fence for the boat to glitch into it. Otherwise, and always going eastward, you get MCPE-58008.
Update: This bug is now being tracked at MCPE-47737.