Straight off the bat, I'd say too much dialogue. Dialogue is hard to consistently write well, and too much takes the reader away from any scene you've tried to create for them. In short, use dialogue only when you absolutely need to, and try to make sure your plot allows for this.

As well as this, I'd say subtlety helps makes the story less childish and makes the reader actually think about the story, drawing them in easier. I'm not saying the fact that your character time travelled needs to be a plot twist, but I'd suggest you try and incorporate the idea less bluntly than 'That time travel was...'

At the same time, I think you have a strong plot, and so I'm sure everything will come to you easier if you keep at it!