How does the timing on the Kingpin's special enhancement work if Taskmaster is on click 2 and he takes an action to turn to click 1 for the precision strike or click 5 for the RCE?

I believe task master can use all the things. The break down:

Beginning of turn I put taskmaster onto click 1. Then I declare a ranged combat action while adjacent. I am using enhancement. I check for one of the criteria of the special power. Since I have precision strike I can use everything. I make my range combat attack.

As soon as taskmaster can use any of the listed powers/abilities he can use all of them while adjacent to kingpin.

Also note that the turning of taskmaster's dial is not an action. It's just something you can choose to do at the beginning of your turn.

Close, but not quite. Kingpins effect checks constantly, not just when Enhancement is being used, and not just during an action. Otherwise, it wouldn't actually allow someone to activate RCE.

So, its: Beginning of turn, put Taskmaster on click 1/5. He can now use all the listed powers/abilities while adjacent to Kingpin. Then you can give him a Ranged Action to make a normal attack, or a Power Action to activate RCE.

At least I was close. Thanks for clarifying it!