Ok FYI I am not stupid, just mislead. You can sell carrots, but it says you cannot. Someone explain.

The long explanation is that when you try to /sell carrot, the Bukkit plugin that processes the shop commands is probably interpreting your command as "/sell 141" rather than "/sell 391".  Carrots (along with several other items) might use a common name between multiple ID's within the game: In this case, a carrot (item) is given an item ID of 391 to represent a carrot as dropped and held in inventory, whereas a carrot (block) is given a block ID of 141 to represent a carrot crop as it would exist when planted on tilled farmland and progressing through it's eight stages of growth. 

While the game uses the name Carrot for both the block and item, when creating a chest shop, using 391 or 392 on line four will cause the sign to read 'Carrot Item' or 'Potato Item' - I can only assume that a chest shop sign with 141 or 142 on line 4 would read simply 'Carrot' or 'Potato'.

Of interest is that when carrots and potatoes were first implemented, harvesting planted crops would sometimes drop the 'block' as well as the 'item', so for a brief while, the ID 141 and 142 blocks were obtainable in survival mode via this bug.  In inventory, they used the texture of the respective block in early stages of growth, and had no use in crafting or as a food item.  You could, however, replant the 'block' and it would grow through the stages to maturity just as is you'd planted it's 'item' counterpart.  Ordinarily, the only way to obtain these 'blocks' would be with the /give command or similar workarounds.