It ends up being not particularly game breaking.
- If you copy Den of the Wolf, you won't get, for example, 3 Dominance phases in a row. Triggering Den of the Wolf repeats the current phase at the end of that phase. So either the original or the copy can create an additional phase, but not both since the second one would no longer be at the end of the "current" phase that it was triggered in. (This is actually the same reason we needed a ruling on multiple Epic Battle cards. I'm not sure we can apply that ruling here.)
- Copying Patchface in a Joust game would have a similar effect. The original and copied "must remain revealed" effects run parallel and have the same duration, so copying doesn't gain you anything. In a Melee game, you could choose another opponent, but that would be no different than two different players using their own copies of Patchface in the same round. Pretty much the same thing with Tyrion's Chain in Melee. They could make one round very one-sided, but in melee that's not particularly game breaking (or uncommon - careful selection of Titles can do it, too).
Moral of the story, BTW, is that yes, they can be copied. Copies of "once per game" effects do not exceed the limit any more than copies of "once per phase" effects exceed their limit - reason being that you are not triggering the "once per game" effect a second time.