For us they seem to delay the shipping the item yet still claim two day shipping. For example ordering around midday (Pacific timezone) on a Thursday often results in the item not shipping until later on Monday, which then arrives Wednesday but more often Thursday morning. Every step on the way can be contrived as "two day", but it really took a week and that is the number we care about. We likely won't be renewing Prime.

Amusingly there are also those orders of things you don't care about getting immediately. Those seem to come fast, often less than 24 hours from ordering. Amazon doesn't know which items fall in which category (their media $1 credit is not worth it). Nor do they seem to notice breaking their own promises and proactively doing something about.