Lines will disappear/replicate when I do new line operations in vim.
Before: https://puu.sh/rvLMZ/3e93f9809e.png
After: https://puu.sh/rvLV2/722b4a8c8c.png

I have the same behavior when using hyperterm with vim version 8. However when I start vim without configuration, love and plugins I can't reproduce the behavior.
Please also test with:
vim -u NONE

And also no problems when I set :syntax on

Can confirm everything renders properly when I follow your suggestions. Thanks for pointing this out. It's still a shame I can't use my vim plugins/configs...
I did some more playing around and I found that it's just the line numbers that are ruining everything for me. If I :set nonumber then I don't see any rendering issues anymore, even with all my plugins/configs turned on.
Seeing the same.
I also see strange rendering issues in VIM 8.0 on macOS Sierra.
I think it might be related to having NERDTree open. When I close NERDTree I don't have the issue anymore.
I've also noticed that problems present themselves when I have an emoji character in the buffer. (I use emoji's to signal syntax or linting problems with syntastic)

Note how the tap line is slightly misaligned because of the emoji in the same line

@tamoore Can you confirm that the problem goes away when you turn off all your plugins (regardless of emoji or no emoji)?
Yeah the problem isn't present when all plugins are disabled.
Although, having said that, I suspect the issue isn't with either vim or the plugins it seems like a rendering issue with regards to the strange emoji character.
I tried just copying and pasting an emoji in the prompt to see what effect it would have. It seems that if you paste it then try to add any characters before it (the emoji), it's a little borked. See below:
Command | Result
------------ | -------------
<paste> 😀 | 
← ← ' | 
<delete> <delete> <delete> | 
The unicode chars are wrapped with a span and their width is 1 column. There is a parsing issue i guess, because sometimes i see spaces in the span wrapper of unicode char. As you see in the screenshot, the space after folder icon is inside the span wrapper and folder is sticked to text.

Hey there, please try again with the new Hyper v2 release and open a new issue if the problem stills exists. Thank you!
Most helpful comment
I did some more playing around and I found that it's just the line numbers that are ruining everything for me. If I
:set nonumberthen I don't see any rendering issues anymore, even with all my plugins/configs turned on.