How can I allow placement of certain blocks in Minecraft adventure mode?
This if fairly easy to do, but the command required is very long.
The way you should do this, as other answers have already pointed out, is by putting CanPlaceOn tags onto the item. There's no easy way to do this once the items are already in the player's inventory, so instead you should do it for the dropped item entities with /data.
CanPlaceOn is also fairly annoying in that you need to name every single block you want to be able to place the block onto. I used the block name table from the Minecraft wiki, and wrote a script to convert the names into the right format.
Overall, the command you need to run on a fast clock is:
/data merge @e[type=Item] {Item:{tag:{CanPlaceOn:["minecraft:air","minecraft:stone","minecraft:grass","minecraft:dirt","minecraft:cobblestone","minecraft:planks","minecraft:sapling","minecraft:bedrock","minecraft:flowing_water","minecraft:water","minecraft:flowing_lava","minecraft:lava","minecraft:sand","minecraft:gravel","minecraft:gold_ore","minecraft:iron_ore","minecraft:coal_ore","minecraft:log","minecraft:leaves","minecraft:sponge","minecraft:glass","minecraft:lapis_ore","minecraft:lapis_block","minecraft:dispenser","minecraft:sandstone","minecraft:noteblock","minecraft:golden_rail","minecraft:detector_rail","minecraft:sticky_piston","minecraft:web","minecraft:tallgrass","minecraft:deadbush","minecraft:piston","minecraft:piston_head","minecraft:wool","minecraft:piston_extension","minecraft:yellow_flower","minecraft:red_flower","minecraft:brown_mushroom","minecraft:red_mushroom","minecraft:gold_block","minecraft:iron_block","minecraft:double_stone_slab","minecraft:stone_slab","minecraft:brick_block","minecraft:tnt","minecraft:bookshelf","minecraft:mossy_cobblestone","minecraft:obsidian","minecraft:torch","minecraft:fire","minecraft:mob_spawner","minecraft:oak_stairs","minecraft:chest","minecraft:redstone_wire","minecraft:diamond_ore","minecraft:diamond_block","minecraft:crafting_table","minecraft:farmland","minecraft:furnace","minecraft:lit_furnace","minecraft:standing_sign","minecraft:ladder","minecraft:rail","minecraft:stone_stairs","minecraft:wall_sign","minecraft:lever","minecraft:stone_pressure_plate","minecraft:wooden_pressure_plate","minecraft:redstone_ore","minecraft:lit_redstone_ore","minecraft:unlit_redstone_torch","minecraft:redstone_torch","minecraft:stone_button","minecraft:snow_layer","minecraft:ice","minecraft:snow","minecraft:cactus","minecraft:clay","minecraft:jukebox","minecraft:fence","minecraft:pumpkin","minecraft:netherrack","minecraft:soul_sand","minecraft:glowstone","minecraft:portal","minecraft:lit_pumpkin","minecraft:unpowered_repeater","minecraft:powered_repeater","minecraft:stained_glass","minecraft:trapdoor","minecraft:monster_egg","minecraft:stonebrick","minecraft:brown_mushroom_block","minecraft:red_mushroom_block","minecraft:iron_bars","minecraft:glass_pane","minecraft:melon_block","minecraft:pumpkin_stem","minecraft:melon_stem","minecraft:vine","minecraft:fence_gate","minecraft:brick_stairs","minecraft:stone_brick_stairs","minecraft:mycelium","minecraft:waterlily","minecraft:nether_brick","minecraft:nether_brick_fence","minecraft:nether_brick_stairs","minecraft:enchanting_table","minecraft:end_portal","minecraft:end_portal_frame","minecraft:end_stone","minecraft:dragon_egg","minecraft:redstone_lamp","minecraft:lit_redstone_lamp","minecraft:double_wooden_slab","minecraft:wooden_slab","minecraft:cocoa","minecraft:sandstone_stairs","minecraft:emerald_ore","minecraft:ender_chest","minecraft:tripwire_hook","minecraft:tripwire","minecraft:emerald_block","minecraft:spruce_stairs","minecraft:birch_stairs","minecraft:jungle_stairs","minecraft:command_block","minecraft:beacon","minecraft:cobblestone_wall","minecraft:wooden_button","minecraft:anvil","minecraft:trapped_chest","minecraft:light_weighted_pressure_plate","minecraft:heavy_weighted_pressure_plate","minecraft:unpowered_comparator","minecraft:powered_comparator","minecraft:daylight_detector","minecraft:redstone_block","minecraft:quartz_ore","minecraft:hopper","minecraft:quartz_block","minecraft:quartz_stairs","minecraft:activator_rail","minecraft:dropper","minecraft:stained_hardened_clay","minecraft:stained_glass_pane","minecraft:log2","minecraft:log2","minecraft:acacia_stairs","minecraft:dark_oak_stairs","minecraft:slime","minecraft:barrier","minecraft:iron_trapdoor","minecraft:prismarine","minecraft:sea_lantern","minecraft:hay_block","minecraft:carpet","minecraft:hardened_clay","minecraft:coal_block","minecraft:packed_ice","minecraft:double_plant","minecraft:prismarine","minecraft:barrier","minecraft:red_sandstone","minecraft:sea_lantern","minecraft:iron_trapdoor"],HideFlags:16}}}