One good technique to have in mind when making a set of characters for a game is to not have any two characters with completely compatible goals. This fulfills a few of the stated goals: It makes each character unique in the game. It makes each player have to be constantly facing questions and making meaningful decisions about who to work with. It also means that the player will need to be active to see their goals fulfilled: they cannot completely rely on anyone else, so they need to do things themselves (which encourages people being active, which is good). and it encourages you as larpwright to make enough distinct goals and subplots and such that each character has at least two or three things going on, which makes for a dynamic set of characters and a fun game.
So each character may agree with any other character on some goals/tasks/etc. But they won't agree with any character on everything. This means that there is a potential for conflict between any two characters. Which means that no one can totally trust any other character.
If two characters have identical sets of goals, then they're likely candidates to be collapsed into a single character. In play, these two characters would wind up doing about the same thing anyway, so why have two people doing that when you could just have one? Or if you don't want to combine them for some reason, then changing one to have different priorities or motivations in some way can make for two similar but not identical characters. Then they can have the fun interaction of working together on most things, but conflicting on something else.
If you have a bunch of characters who can trust each other completely and work together to achieve their goals, they're likely to band together when they realize this and dominate the game. Other larps call this problem the "Good Guy Mobs". Once a single group outnumbers the next biggest group, then they wield a lot of power and can easily unbalance the game in their favor. This makes for a game ending quicker than it should, without as much entertaining interaction as might be desired. Preventing Good Guy Mobs from forming helps keep the game entertaining for everyone.
Conflicts don't have to be huge, life or death things, either. In the Scifi Mystery game, the leaders of each groups each had their own priorities (research versus exterminating threats versus rescuing any survivors) and were in disagreement about who was the top ranking official. But they generally agreed that research, rescuing survivors and exterminating threats were all valuable goals. The conflict there would be what to do if one goal pointed in one direction and a different goal pointed a different way.
Different characters can disagree about how to achieve a goal, too. In the Bloody Forks game, George Washington wanted the french out of the Pittsburgh region. Any sensible observer would probably recognize that violence would provoke the French and lead to war rather than leading to the French clearing out. Washington's ally Half-King Tanaghrisson wanted the French, but he wanted it for personal, emotional reasons. so he was much more willing to use violence against them to get his revenge, regardless of what the consequences would be. This means that Washington can get help from Half-King in achieving his goal, but needs to monitor his ally's efforts to make sure they were both on the same page.
So: having differing goals means each character's interactions with every other character will be interesting and at least have the potential for dramatic interactions. In actual play, some of these differing goals never come to light. But enough of them will that it will keep the game dynamic, provided that you've packed the relationship between characters with enough tension and enough conflicting goals.