Jack offed a few other unarmed bad guys to avenge a fallen friends/ loved ones ...
Ssn 1 ... Dennis Hopper (whatever his name was). Jack thought Kim was dead and shot him unarmed for the percieved death of his daughter. Pumped a whole clip into the guy.
Ssn 3 ... Nina Myers. She had no further information to offer, and was responsible for murdering his wife. Bang.
Ssn 5 ... Trigger man for David Palmer assassination, bombed Michelle Desslers car. The guy gave Jack the information he needed in exchange for transport to a hospital. Jack shot him in the head.
Ssn 5 ... Christopher Henderson. Responsible for the (somewhat overstated) death of Tony. Henderson helped raid a submarine and was out of ammo, and Jack executed him.
The execution of Dana Walsh was not quite unprecedented. That being said ... I’m thinking there’s going to be a 4-hour bloodbath through the end of this series. According to the preview, the Renee trigger-man is going to get the working end of a blowtorch.
SnakeDoc
A reason did occur to me though and it let's Jack off the hook for taking Cole's satisfaction away. Jack could see from his own long experience that it would save Cole a lot of grief in the long run if Dana just ceased to exist. Not a justification but the best I could do for an excuse.
Then again maybe it was just the bullet wound, cracked ribs and sundry deep bruises irritating him and Dana's smart mouth was the last straw. I know I wanted to shoot her. LOL