This is not a complete list of bugs but I have described all the bugs of which you can take advantage (and they can always be reproduced).
When you have started to chop wood before building a town hall or lumbermill, you'll get some extra lumber (100 for town hall, 125 for lumber mill) even if the peon did not finish his job.
You don't even have to wait until he's started, just right click on the forest and build a town hall afterwards.
Using this bug is crucial at low resource levels, and everyone takes advantage of it nowadays.
This bug works with gold as well when building a town hall, but is more tricky to be used (especially over modem with slow response). Because you'll want to build your town hall as close to the mine as you can, it is quite probable that the peon walks into the mine and takes a break :-) there. Another reason not to use gold is because you can get gold very easily but you'll have to wait a long time to get more lumber.
The fog of war is not as impenetrable as it seems. You don't see any units but you can see buildings; their status won't be updated, though. However, this doesn't work for wood and walls. Trees will keep disappearing through the fog of war, and you'll see where new walls have been built. This is quite important when building a new town; unless everyone knows where you are, you shouldn't build any walls in there and avoid chopping lumber if you can. That will keep your expansion secret.
I've also found out that you can see whether a building explodes under a blizzard through the fog of war even if it is out of the wizard's sight. The building won't disappear afterwards until you have verified it by getting close enough to it, but if you keep watching, this might help you to find out whether a tower has been destroyed or not. I think only very few players know that.
I think you've already seen a ballista shooting but no arrow was flying around. This also happens to catapults, archers, axethrowers, destroyers and battleships/juggs. Such a unit misfires if you give them a new target when they were just about to fire. Then, the computer can't switch anymore to the new target, and no shot will be fired. This is fatal in naval battles and otherwise also undesirable. Thus, never keep on clicking on a target or your unit will not fire at all. Also be careful when you've used the "attack" command; if you want to change the target, you should wait until the unit has fired. Using stop to change the target to a random one will also produce a misfired shot. By the way, all units can misfire, even knights and footmen. However, that rarely happens, and you will only be aware of it if you watch the fight well.
|This bug rarely occurs: If you tell a group of sappers/demo squads to destroy a larger building, e. g. a fortress, then, at the very moment when the fortress is destroyed, all the units which formed the group and have survived will explode simultaneously instead of stopping their now pointless attack. Therefore, be careful when using an extra sapper to destroy a castle. You'll not only lose your fifth sapper anyway; the explosion is also a destructive one (unlike when he's killed by an enemy), and it will destroy all units standing nearby which may be yours. (However, you should have an fifth sapper at hand if one of the other four fails.) You should never form a large group of sappers to destroy a building anyway; instead, send them one by one, with about a second pause between them. Like that, they won't destroy each other when one sapper has reached the building and the second one is next to the first one but not yet in range of the building (as shown in the picture; this isn't actually a bug.)||
The two demosquads on top of the red arrows must have been close friends, for they go to death together :-)