Over the years we've seen quite a few "I want to log everything" questions asked for which I listed some
pointers a while ago in several posts. To complement a recent "I want to capture all the operations performed in the terminal" question (thread:
How to Capture a Unix Terminal Session?) I looked for Bash patches. Long story short: Bash 4 can be compiled with syslog support
but still that shell will run as the user who logs in AFAIK. (So depending on your requirements for coverage...