Key names and values must be separated with a colon; your id tags are missing that colon.
You are also using an invalid quotation symbol ”, when it needs to be " instead.
Fixed command, removing excess keys (list elements do not use keys, despite the output shown).
/entitydata @e[type=chest_minecart,name=Command_Cart] {Items:[{Slot:0b,id:"minecraft:written_book",Count:1b,tag:{pages:["{\"text\":\"/gamemode @p 0\"}"],author:"MeTheCommandCart",title:"Gamemode 0",resolved:1b},Damage:0s},{Slot:1b,id:"minecraft:written_book",Count:1b,tag:{pages:["{\"text\":\"/gamemode @p 1\"}"],author:"MeTheCommandCart",title:"Gamemode 1",resolved:1b},Damage:0s},{Slot:2b,id:"minecraft:written_book",Count:1b,tag:{pages:["{\"text\":\"/gamemode @p 2\"}"],author:"MeTheCommandCart",title:"Gamemode 2",resolved:1b},Damage:0s},{Slot:3b,id:"minecraft:written_book",Count:1b,tag:{pages:["{\"text\":\"/gamemode @p 3\"}"],author:"MeTheCommandCart",title:"Gamemode 3",resolved:1b},Damage:0s},{Slot:4b,id:"minecraft:paper",Count:1b,tag:{RepairCost:0,display:{Name:"Command goes under here"}},Damage:0s},{Slot:12b,id:"minecraft:paper",Count:1b,tag:{RepairCost:0,display:{Name:"Command goes right of here"}},Damage:0s},{Slot:14b,id:"minecraft:paper",Count:1b,tag:{RepairCost:0,display:{Name:"Command goes left of here"}},Damage:0s},{Slot:22b,id:"minecraft:paper",Count:1b,tag:{RepairCost:0,display:{Name:"Command goes above here"}},Damage:0s}]}