In addition to Rampage’s good advice, there was a change in 1.4 that can benefit you. The Angler will “look” in your personal inventory (inventory, piggy bank, safe, etc) and if it contains (for instance) the Fisherman’s Pocket Guide, he won’t give you another pocket guide (if he’s giving out one of the three cell phone pieces). So when you turn in quests make sure the pieces you’ve already received are in your personal inventory (and not in a chest) so that if he hands out another piece it will be different.
Changelog: “Angler’s Quest rewards are now more likely to give you the Info Accessories. Additionally, he will not give you duplicates of an accessory you have in your inventory, unless you already have them all.”