The app store itself should prompt for the reviews, on a reasonable schedule after purchase/download.
Maybe 3 days after purchase for a thumbs-up, thumbs-down initial impression. Two weeks after purchase for an N/5 star review. Two months after purchase for a star rating update and descriptive text review for other potential customers. Six months after purchase, and yearly thereafter, for a star rating update and descriptive feedback aimed at the vendor, such as pain points and enhancement requests. Each time, allow the user to opt-out of review request nagging.
This would also allow a chart of user satisfaction over time, filtering reviews by length of ownership, and trends in user satisfaction, especially in response to version updates. I am far more likely to trust a reviewer that has gone from a three-star rating to a five-star rating, over four years of owning the app, and has reviewed other apps from different vendors, than someone who gives it five-stars after a week, has never reviewed anything else, and then vanishes forever.
One would think that the company that developed PageRank could do something similar for review rankings, to weed out review-bots, astroturfers, and straw-purchasers.