I have been using Prime for about a year at work. I was curious so I just checked and I have placed 89 orders in the past six months. Of that I have had three significant problems. We have a store in SoCal that needed a new TV. We shipped a tv to them twice, both times it was returned to Amazon as undeliverable. Both times they tried to deliver it before the store opened, and the store is in a mall. Pretty obvious what time the mall stores open isn't it? The first time they tried to deliver the tv at 9:30, the second time at 9:42. The mall opens at 10.
The other item was a ladder that I needed in CO quickly, so paid for overnight shipping. It arrived three days later. They refunded the shipping with no issues at all. What does annoy me is that to reach someone live, it is a royal pain.
Oh, we did have one more problem. I ordered 350 sets of small screw drivers. They let me order and pay for them all, yet they only had 150 of them on hand. I was promised during a phone call that they rest would be in stock in ten days. Three weeks later they finally arrived.
Still not many issues for the number of orders placed. For the convenience of sitting at my desk and ordering in items for stores throughout the US, it is worth it.