The fix for MCPE-62419 doesn't extend to the client-side. Moving blocks are still full blocks client-side and pistons still don't move you properly lots of the time.
Resulting issues (and how to reproduce):
When standing on non-full blocks, such as slabs, the game pushes you out when the slab is moved.
When standing near the edge of blocks and being pushed up, you get pushed out, but entities don't on the server-side.
Putting an item on a bottom slab/trapdoor and moving it can cause client-server desyncs and ghost items.
Slime blocks don't launch players horizontally most of the time. They do server-side, but the client moves you back, causing a temporary desync. A combination of ice and pressure plates helps visualise the issue.
Expected results:
When standing on a slab and the slab is moved, you should be moved along and not be pushed out.
When standing near the edge of blocks and being pushed up, you should not be pushed off.
When putting an item on a bottom slab/trapdoor and moving it it should behave the same client-side as it does server-side.
Slime blocks should launch you horizontally and it should be the same client-side as server-side.
You are moved in a less buggy way compared to 1.14.20 for two main reasons:
Moving blocks now move half a block at a time and move players half a block at a time. The smaller steps makes it harder for the player to glitch out to the side, like in 1.14.20.
It functions properly server-side, which affects the client somewhat.
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I've added a test world demonstrating these issues.

The second issue, especially, sounds like it could be related to MCPE-65094. It’s possible that the server doesn’t have you standing on the block to begin with.

Well the slime block now bounces entities(at least TNT is) for 3-4 blocks away instade of 6-7blocks horizionally, breaking my tunnelbore machine.XD
Also, players can only be bounced upward for only 5 blocks intead of 6, breaking the slime block elevator.
I hope it can be fixed to let the block bounce entities for 6-7blocks again😃

Affects 1.16.100.57

Upon a little more research, I stumbled upon this: For players, moving blocks adopt their collision box for their future location while they are still in the half extension state. The same can be said with retraction. Entities seem to react to half extended / retracted moving blocks fine and properly collide with them.
In 1.14, this issue was still present for both players and entities, and looking back it seems that entities used to have the same issue.
My guess would be that in order to fix this issue,1. collision boxes of moving blocks need to be properly transitioned when they are in their half extension / retraction state and 2. remove the current temporary fix implemented for slime not launching as a consequence of this behavior (or else behavior as described by @buyifan will persist.)

I cannot reproduce any of the described issues in 1.18.2 Hotfix. This must have been fixed between 1.17.30 and 1.18.0.
This was not fixed in 1.18. It was only fixed in today's beta (1.19.50.20).
All examples provided in the test world work correctly now.

I think the fix in 1.19.50 was for MCPE-160263, as this issue had been fixed and then reverted, so the newer report was made.
[^Moving blocks [1.16.100.51].mcworld]