Any issue with "overlapping" sliding windows in time-series data analysis?
In general I don't see anything wrong with overlapping windows, it might make perfect sense depending on your task. In fact some learning models (e.g. for sequence labeling) do use features based on past data points, which is conceptually similar to having overlaps between them.

However you need to be careful about the fact that this makes data points depend on each other, so of course the preprocessing must be done separately for the training and test set.