When in an alliance, you cannot have treaties with non-alliance members (what about trades?). That makes alliances practically useless and even dangerous. Since nobody uses them, there also might remain some other unknown bugs in the alliance system.
As of patch version 1.74 Alliances have some serious bugs that make their use of limited to no value. One of the major bugs is the voting system. The unfortunate side-effect is that players can be pulled into Alliances against their will and with only one member of the Alliance voting on it. When left in the hands of the AI this can be a game-breaking event. If you are in an Alliance with an AI (or miss your turn in multiplayer and the AI takes your turn for you) the AI can add one of your enemies into the Alliance. If you were sharing anything important, like technologies, your enemy will now have that knowledge.