I wish that there was an optional filter that would hide 1-turn units from Replays and Battle History.
1.
It is really boring to watch a player move around all their 1-turn units without them doing anything. Replays could be more interesting and faster if the animated movement of stacks consisting of a single 1-turn unit could be skipped automatically.
Likewise, seeing a light cav gloriously capturing an undefended village is not as exciting as it may sound, so I would like to be able to skip those battles in replays too.
2.
The same is true for the battle history beyond the last 1-2 turns: whenever I look through the battle history for older turns, I want to find the big battles that tell me about the enemy's stack compositions, hero types and positions and items, etc. Instead, I have to wade through a mass of mostly uninteresting battles about money sites. This is especially true for team games, where it is even more difficult to find the interesting reports among all those team mate battles.
Therefore, it would be nice if the battle history had a marker that would display whether or not the battle featured combatants having a combined worth of at least 3 turns of production (since heroes are valued at 3 production turns for XP, I would guess this would mark battles of single heroes against undefended sites as well). Alternatively, a quick button inside the battle history window that would hide the simple battles would save some mileage on my scroll wheel.