I used to try to get every single shop but now I just get enough plus a few extra to be entered. It bugs me when shops have no clues or have a clue and it goes nowhere so if that's the case, I immediately move on to the next one. Also I wait until the last week of the month to search anymore. Sometimes they will add 'bonus bunnies' about halfway through the month and I don't want to go back and look all over again to find those. I can usually get all 130 or more shops done in 3 or 4 nights.
eta: you shouldn't have to write down shop names/numbers to keep track. You can go into the member area and click on 'shops not visited' to see all the shops you haven't been to yet. I never use their 'preferred order' list.