It was a bit hard to understand right away what it was doing and how to properly use it even with the instructions.
The language dropdown is not clear what it is for, the source language? or the destination? so I can write in whatever language and it gets to that? That's cool but I would mention it.
The UI is quite messy. There is a lot of stuff going on in that page and very little in relevant once I start writing. I would suggest you to look into a more "distraction free" approach and have a little tutorial when the user first visits the writer.
A key shortcut to iterate the latest suggestions would be extremely helpful.
If I start a translation before the older one is finished things start to go weird and this is not too much of an uncommon situation since the translation is not the fastest. If you can make it faster, it would be a huge improvement.
Maybe keep the parts that I translated highlights so I can more easily go back and review them since I might not want to stop writing for each translation I make.
Consider making a chrome plugin, this would make this tool 1000 time more useful.
Keep at it! You are onto something!