I dont belive its a mistake, here is what i think.
You should not consider damage, but damage per second (DPS). So even if the lvl 56 item has higher damage, it might be slower and provide less DPS which is what matters. Alternatively, the lvl 52 weapon could have high main stat value (strength, dexterity, inteligence), while the lvl 56 maybe has none. Main stats are also a great DPS boost at lower levels.