I've been an SN AmEx (classic) card holder since the card has been introduced. Generally speaking I've experienced no problems: had to call once ( 3 or 4 years ago) to get my 5000 miles year bonus posted and that's it. Miles are posted promptly, two days (!) after the date of invoice. So - as with many things - your experience will vary.
I had the card blocked once in the US - a phone call fixed it. I was told that I should notify them before (quote) "travelling to third world countries like the USA or Africa". Priceless.