They looked at one another.
how about jane staring at Tom, Dick and Harry and they staring back at each of the remaining 3?
How can Jane simultaneously stare at Tom, Dick and Harry. She might've had 6 eyes:-)
Each other implies two people.
One another implies more three or more people.
Cyndi has it right.
"To love is not to look at one another, but to look together in the same direction" Antoine de Saint-Exupery