I think Greg hit it, but here's an example:
Some friends of mine (civil engineers...I mix with a bad crowd

recently had an issue where they had designed a non-traditional joint in a building and someone questioned the accuracy of their RISA analysis. This building was extremely complicated, but their beam model did a good (and very fast) job of calculating reactions in the beams...shear and moment diagrams, etc. It was, as Greg mentions, the joints that were the area of concern.
In the joints, they had connected several beams by welding "boxes" with multiple faces that lined up to where the beams would come in. I extracted their loads from RISA and modeled the detailed joint using very refined plate elements to get a detailed load path. It showed some issues and how to quickly and easily resolve them.
I love FEA...bit of a fanatic...play with software in my off hours after the children go to bed. NEVER FORGET...it is a tool. Don't bring a rack to dig a hole...don't bring a knife to a gun fight. I support three different packages that, in my opinion, are useful for three different functions. One is very inexpensive with great tools for importing and cleaning up CAD models. One I've used for over a decade...I'm very fast with it and it handles most of the problem types that I may need. The third has very powerful contact algorithms and an explicit solver and runs a good bit more efficiently than most softwares (don't need a supercomputer to run significant contact).
Make sure you know what types of problems your tool can address, and learn the right way to use it to its fullest capabilities. Don't try to use it for something that it isn't designed to do, and make sure you are using it correctly by periodically running a problem that you CAN hand calculate and comparing to your results.