What could cause all the breakers on the left side of my panel box to trip?
This has happened to me.  You may have just manually tripped the breakers when you were putting the cover back on.  It doesn't take much force to trip the breaker.

It's unlikely that an electrical mis-wiring caused this, because each side of the box is fed alternatively by both of "hot" feed.  Say you have split phase 1 and 2.  The left side of your box will be fed by phase 1, 2, 1, 2, etc.  The breakers on the left side have nothing in common with each other that they don't also have in common with the right side.