(1) values,Of course, commonalities in some of these areas are noticeable more immediately than others. A similar sense of humor is quickly apparent, and shared interests are usually discovered early on. Whether values align is a much subtler question, especially since we aren't always aware of our own deepest values, but also because most of us aren't likely to talk about our fundamental values with a person we have just met. Revealing the inner workings of ourselves makes us vulnerable and can be overwhelming or imposing for the other person, so we don't do it right away. We work on the surface.
(3) sense of humor,
(4) style of communication, or
(5) emotional reactions (personality).
Likewise, personality and communication style aren't always immediately clear, because in order to function in society, we must all adapt our personalities and communicational styles. The persona that initially comes across, while not necessarily "fake", is often not the person's most natural self. Rather, it is the vision of the self constructed in order to guard the real self and work effectively with the surrounding individuals. (Extroverts don't have to put forth as much effort to connect with others as introverts do, so their personalities don't intrinsically pose problems for functioning in social settings. The "successful" introvert, though, probably isn't seen as an introvert, but rather as friendly and confident--characteristics which, though genuine, do not come naturally.) The outer self is as much a function of the surrounding environment as of the inner reality.
Preferred communication style may also be hidden. For instance, take a person who comes from a background that fostered indirect communication (such as Japan), and thus prefers to communicate indirectly, but who interacts primarily with people who communicate more directly (such as Americans). This person would have to adapt their day-to-day conversation style to function effectively, so they would appear to also have a direct communication style. But underneath, their natural communication style is quite different. Yet another complication is that a person who communicates very directly is unlikely to pick up on their conversation partner's indirect requests, and may not even notice that there is a misalignment.
So initial clicking tends to take place on the surface level: interests and sense of humor, and (to some extent) communicational style.
But what happens when two people are really well-matched on the surface levels but not on underlying values? They feel like they click, but ultimately they discover that they don't understand each other's core ideas. This can be problematic, because the surface level clicking has already created a strong bond by the time the issue of disparate values comes up...
In any case, on a day-to-day level, it's easier (though not necessarily more satisfying) to interact with people who share your interests, humor and communicational style but not your core values than the reverse--people who care about the same fundamental things but don't understand your attempts to communicate with them.