I created a template recipe template in Composer and added ol and ul blocks and there's no left padding:

https://monosnap.com/file/WfnSkARWQ1MIqfKXkNSr4F7yppIqKS

I know it looks different when published but composer is supposed to be WYSIWYG right?

Also notice the heading block, the top and bottom margins are not set.

Another one, when I add blocks, it auto add it on top of all blocks that I previously added. I will have to drag it down and it will mess up the formatting of other blocks when I accidentally drop it inside a block.

- Maybe after selecting a Block, instead of auto adding it on top it kind of make the user select where to drop it but default it at the bottom. I don't think people create things from bottom to top.

When editing an active Block there is a Move at the bottom the border but it is not the move handle, that is confusing! Take note the Duplicate and Delete works but not the Move. I will have to move the mouse on almost top of the block to get the move handle.

https://monosnap.com/file/IQoT9O8JIEYL5v1Cs5Fk0jhF5ofJi7

I've tested on your site, it seems work fine when i drag those new block into blog content, you can watch my video here : http://take.ms/gnfMo

But i would suggest you to use click block what you would like to add then select which block position you would like to put, for example : http://take.ms/TU5FUM

If you already watch my video, i did tested move button, it seems work fine for me.

What I did is to simply click on a Block, I did not drag to a location in the canvas. That was what I'm pointing out. The default behavior when you just click on a Block is it adds the new block on top of the canvas.

So you're supposed to select a location after clicking on the Move button. There's no user indication what you are supposed to do after clicking. I mean, nothing in the UI changed after clicking the move button for users to do. Maybe it needs visual cue to let users know the next action.
Update: I upgraded to v5.1.13 and that's what I'm talking about, visual cue! Thank you guys for adding that.