Dave,
As a general rule, you won't have many problems with any safe from any manufacturer. These things aren't overly complicated in how they function. Some manufacturers and retailers like to point out "issues" that don't really exist in the real world.
In addition to dealing with the products I sell, I also handle warranty work for several other manufacturers. The vast majority of warranty related calls that we get for gun safes are related to electronic locks. If you avoid one of those, your odds of having any problem of any type are pretty low.
As far as AMSEC specifically, I have had one warranty claim out of all of the safes I have sold the last 5 or 6 years. A customer had purchased a vault door and left it outside beneath a tarp. This caused damage to the paint, and the electronic lock. Even though it was the customer's fault, AMSEC replaced the entire door at no charge. I have never had a mechanical failure on an AMSEC gun safe, and rarely see them on the commercial products.