Everything that moves this story and all the characters along is a series of improbable coincidences. Not just the main characters, but even the minor detective character finds Max and Vincent by coincidently seeing the smashed up taxi on a security screen. What's funny is Vincent makes a point by saying how big and crowded Los Angeles is, but everyone just comes together when the story needs it to.
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I disagree. Detective Fanning was the handler for some of the witnesses Vincent had been hired to kill, and he knew well enough where they all were that evening. It's not a stretch that he'd catch up to them over the course of the evening.
The one example you mentioned isn't improbable.
Improbable coincidences don't automatically make a movie bad as many seem to think. Sometimes things do just happen in a certain way, and because of that, you have a movie, otherwise, it'd just be another day on the job.
Same could be said of Heat but you just have to go along for the ride and enjoy the awesome action scenes.
shareAll movies are like that, because life is somewhat like that, but movies exaggerate it.
I was on vacation in Guadalajara MX when I was a kid, and we are strolling down one of its streets and I saw one of my Jr. High classmates on the other side of the street. What were the chances?
Or, have you ever heard a word for the first time, and then a few minutes later you hear it again for the first time in your life.
Coincidences happen, especially in movies.
Indeed. Many coincidences are not as unlikely as we would believe. Famously, in a room of 30 people, there is a better than 50% chance that two of the thirty will share a birthday. When it came to your chance encounter in Mexico, your brain classifies it as meeting someone from junior high, but in reality, you would have been equally surprised if you met anyone from high school or elementary school (or outside of school altogether), but the brain says, "I only knew X people in junior high, and here I am meeting one of them."
While the writers shoe-horned many chance encounters, they were generally plausible enough to push on. The morgue in the hospital so that Fanning and Vincent are sharing an elevator? OK, fine, whatever. Vincent scopes out his last hit, so he happens to get into the same cab as Annie? One of the tricks was Vincent initially passed on Max's cab, but the latter reeled him back, so it wasn't straight A to B; there was the appearance of agency even though the story demanded those two characters come together.