Why the heck is the FBI investigating car crashes in LA? Or even murders? (that are not even serial killer-related)
Early on, they make some effort to justify the cases. The murders take place on land that "happens to be owned by the federal government" or the victim is an undercover FBI agent.
Issues regarding the plots of the criminals are often filled with this as well. How is it even remotely possible for bank robbers to play minesweeper with banks? How is it possible that The Tipping Point can be applied to a sniper spree in LA? Wouldn't a prison check a fuel truck to see if it is full before allowing it inside the prison?
Charlie's calculations occasionally hinge on the people he's after being as smart as he is. Apparently, random criminals can intuitively make the mathematically ideal move when planning a crime. During the bomb plot in Season 1, for example, Charlie needs detailed maps of the city and help from both a physicist and a city planner to have all the information needed to find the ideal location for a dirty bomb. The bombers put it in that exact position.
Well, he was specifically looking at variables that people intending to use a dirty bomb would be looking at, things like wind speed and population density and even then, he could only narrow it down to two likely place. The city planner contributed by providing the final location because he's familiar with what the places are actually like.
What was made worse was that in that episode it was the same plot as Die Hard 3, in which it was a robbery that used a terror threat in order to serve as a distraction. The problem was that it required the FBI to figure out where the bomb was planted without a threat ever being given. While Charlie was obviously able to figure it out, there was no way for the thieves to know this ahead of time.
How does Charlie input the sometimes hundreds of thousands of data points he needs for his equations in a single night?
Why does Charlie have so many chalkboards just laying around the house? Enough to basically re-wall the garage with? Professors and teachers don't take their chalkboards home with them... but remember that Alan owns the house, and he's a retired City Planner/Architect. They frequently DO have chalkboards and drawing easels and such in their homes to go over projects on. Combine that with Alan having to raise Charlie-the-prodigy from a young age, and it's no wonder the house is filled with things to write on and erase over and over... otherwise, little Charlie would have gotten into the drafting paper and written all over the walls!