I have had issues with American Express customer service on my American Express SPG Preferred Card. The core issue was very simple - one of fraud concerns, and American Express needing to verify my identity. I respect and acknowledge that credit card companies should take all necessary steps to ensure my identity is not compromised. However, there were a couple key lapses in customer service which has made my experience extremely frustrating. 
First, the customer service department has repeatedly shown a lack of respect for my time. I have stressed to the customer service department that there are only a few windows when I can attend to this issue, since I have a full time job. I requested that, before trying to call me on the phone, they schedule a time to speak. So far, I have been promised phone calls at four separate time slots, usually at about XXXX Eastern Time ( since I can ensure that I am near my phone then, after the work day ends ). American Express has NEVER called me back at the scheduled time. Instead, customer service calls when I am in lunch meetings, or in a meeting with my boss, or occasionally when I am trying to rush work in the afternoon. Despite repeated assurances that they will honor the next appointment, I have not once gotten a call at a scheduled time. In addition, some of these calls just have not taken place at all. I waited about two weeks for a call from the fraud protection service, after being told it would take two days for them to respond. There was no phone call. Since the customer service department could reach me, it is absolutely baffling that another department could not. My conclusion is that the company simply does not value my time, or keeping to appointments. 
Second, the consumer care professionals have been unable to answer basic queries, and have not taken the time to review the case, forcing me to go through a lengthy process of repeating myself every time I contact them. The first time I contacted them, I did so late at night, since this was the only time I could attend to the issue. However, after navigating several robot menus, and waiting on the line for another five to ten minutes, I received a message that the department I was trying to reach was closed. When the online customer service assured me it would be open, I called at least XXXX or XXXX numbers, only to find that all these departments were closed. The customer service online repeatedly insisted that the departments would be open. Only after finally speaking to a manager was she able to transfer me to a department which knew that the department I was actually trying to reach was closed. The process took about 3 hours. I have gotten increasingly frustrated with this process over the weeks I have been in contact with American Express, and have asked their customer service department to come up with a solution such that I can find a convenient way to verify my identity without having to travel out of the office. When they finally do contact me the customer service representative puts me on hold for XXXX minutes while reviewing my case, then refers me to another department. In many cases, I have had to repeat my case again. 

Third, they have not proposed solutions to genuine issues, merely citing procedure. The fraud team said it would call to verify my identity. It either did not make this call, or made it at an inappropriate time when I could not answer. However, they made no effort to contact me via any other means. They have since asked me to travel to a notary to get my information notarized. As I am travelling, I do not have time to make this trip within the time limit they have stipulated. I was simply told that the card would then be cancelled. When I raised a concern that the promotion I signed up for might have expired by the time I resolved these issues, I was told there would be no compensation.