Dropper into minecart offset by .5 of a block in negative x and z direction

By looking at Minecraft's source code using Forge, I have determined the issue: Droppers, when looking for an inventory at a position, use the block's -x, -y, -z corner to search, while hoppers use the block's center. Because droppers directly use TileEntityHopper's getInventoryAtPosition method, this causes the dropper's searching location to be offset in the -x and -z direction. The fix is simple, and only requires one line to be changed:

BlockDropper.java:
...
    protected void dispense(World worldIn, BlockPos pos)
    {
        BlockSourceImpl blocksourceimpl = new BlockSourceImpl(worldIn, pos);
        TileEntityDispenser tileentitydispenser = (TileEntityDispenser)blocksourceimpl.getBlockTileEntity();

        if (tileentitydispenser != null)
        {
            int i = tileentitydispenser.getDispenseSlot();

            if (i < 0)
            {
                worldIn.playAuxSFX(1001, pos, 0);
            }
            else
            {
                ItemStack itemstack = tileentitydispenser.getStackInSlot(i);

                if (itemstack != null && net.minecraftforge.items.VanillaInventoryCodeHooks.dropperInsertHook(worldIn, pos, tileentitydispenser, i, itemstack))
                {
                    EnumFacing enumfacing = (EnumFacing)worldIn.getBlockState(pos).getValue(FACING);
                    BlockPos blockpos = pos.offset(enumfacing);

// ===========================================================================================
//                  IInventory iinventory = TileEntityHopper.getInventoryAtPosition(worldIn, (double)blockpos.getX(), (double)blockpos.getY(), (double)blockpos.getZ());
                    IInventory iinventory = TileEntityHopper.getInventoryAtPosition(worldIn, (double)blockpos.getX() + 0.5, (double)blockpos.getY() + 0.5, (double)blockpos.getZ() + 0.5);
// ===========================================================================================

                    ItemStack itemstack1;

                    if (iinventory == null)
                    {
                        itemstack1 = this.dropBehavior.dispense(blocksourceimpl, itemstack);

                        if (itemstack1 != null && itemstack1.stackSize <= 0)
                        {
                            itemstack1 = null;
                        }
                    }
                    else
                    {
                        itemstack1 = TileEntityHopper.putStackInInventoryAllSlots(iinventory, itemstack.copy().splitStack(1), enumfacing.getOpposite());

                        if (itemstack1 == null)
                        {
                            itemstack1 = itemstack.copy();

                            if (--itemstack1.stackSize <= 0)
                            {
                                itemstack1 = null;
                            }
                        }
                        else
                        {
                            itemstack1 = itemstack.copy();
                        }
                    }

                    tileentitydispenser.setInventorySlotContents(i, itemstack1);
                }
            }
        }
    }
...

This was fixed at some point

After trying snapshot after snapshot, it seems like this was fixed in 17w47a

Great work! I've updated the ticket to reflect that 🙂