I always thought some of the best episodes of each series involved aliens or an alien device causing the crew to turn against the captain or something similar.
This could make for a really unique mission if implemented well. Just think of all the time we spend upgrading the weapons, armor and shields of our officers. This could lead to a pretty epic fight if you had to battle your own bridge officers or at least stun them long enough to cure the alien neck parasites/alien mind control game/alien energy parasites, etc.
Having to fight them on your own bridge might even be a great surprise way to implement this as a "shocker" moment.
Along those lines, having to face evil, mirror universe versions of yourself and officers (maybe even your ship) could be a pretty epic battle too.
I guess the point of both these ideas would be making you actually REGRET all the upgrades you put into your own people when they turn on you.