Spoilers - how we know they are one of the same through the film

The zip code on Richard Chesler's (Zach Grenier) business card is 198090 (shown briefly in the scene where The Narrator beats himself up in the office). In the shot where we see Tyler Durden's business card (just before The Narrator calls him), The Narrator's thumb is hiding the 6th digit. All we are able to see is 19808...then it's all thumb. 

Tyler appears in the film five times before we clearly see him on the moving walkway at the airport. In the first four appearances, he flashes on screen for a single frame (1/24 of a second) and only when the Narrator has insomnia:

• at the photocopier at work;
• in the corridor outside the doctor's office, when the Narrator learns about the testicular cancer support group;
• at that group's meeting;
• as the Narrator sees Marla leaving a meeting but doesn't follow her.

He can also be seen as a waiter in the presentation video of the hotel (he is the furthest waiter on the right). 

At the airport, the Narrator says "Could you wake up as a different person?" and the camera briefly follows Tyler. 

When Tyler and the Narrator are fighting and gather a crowd, no one intervenes, but instead look rather bemused. 

After the car crash, as Tyler nurses the Narrator back to health, the Narrator has a bruise on his head. When the Narrator wakes up the 'next morning' the bruise is completely gone. Whilst some see this as a continuity error, others argue that it indicates more time has passed than just one night (in fact, the Narrator wasn't asleep at all, he was all over the country setting up fight clubs). 

The Narrator wanders the house while Tyler and Marla noisily have sex upstairs. When the detective calls and the Narrator answers the phone, the sounds of the lovemaking instantly stop. 

On the airplane the Narrator mentions that they have the exact same briefcase. And although Tyler opens his, we never see the contents of the Narrator's. 

When entering Lou's Tavern, the Narrator enters first and the guy out the front only acknowledges the Narrator, as though Tyler doesn't even exist. 

When going to the convenience store where Raymond K. Hessel works, Tyler gets the gun out of the Narrator's bag. The Narrator obviously didn't know the gun was there, indicated by his astonishment "Is that a gun?", despite the fact that it's his backpack. 

When Lou sees the Fight Club members in the basement of his restaurant, Lou punches Tyler in the stomach. When Tyler gets punched, you can see the Narrator double over slightly as if he too was punched in the stomach. A few shots later, Lou kicks Tyler in the face while he is kneeling, and in the background we see the Narrator's head go back at the moment of impact. 

When Tyler and the Narrator hit the first car with baseball bats, Tyler hits first, but the alarm is triggered only after the Narrator hits. 

Chuck Palahniuk revealed that when he wrote the book, he did not actually know that Tyler and the Narrator were the same person until he was two thirds of the way through writing the story, at which point he noticed that they acted together as one person and chose to finish the story as such. 

When the airport employee "lends" Tyler the car, the Narrator and Tyler get in through the same door. After the crash where Tyler was driving, Tyler pulls the Narrator out of the driver's side of the car. 

When the airport valet lends Tyler and the narrator the car, while addressing "Mr. Durden" he is looking straight at the Narrator. 

When the Narrator enters the house prior to seeing the news report of the happy face on the building, he is carrying one of Project Mayhem's folders. 

When the narrator gets on the bus with Tyler, he only pays the fare for one person. 

When Tyler and the Narrator are on the bus, the long-haired guy pushes past Tyler without a word, then says "excuse me" as he pushes past the Narrator. 

The buildings that blow up in the end are all Fox-owned buildings digitally composited into the shot. It was feared that they would invite legal action against the production if they portrayed real credit card companies blowing up. 

When Tyler Durden calls The Narrator back in the phone booth, the camera slowly tracks in towards the phone. On the left of the phone, a notice can be seen saying "No incoming calls allowed." 

The Group Leader (George Maguire) begins his speech at the Testicular Cancer support group by saying, "I look around this room and I see a lot of...". Later, when Tyler makes his 'Middle children of history' speech, he begins, "I look around this room and I see a lot of..." 

The shot of The Narrator shooting himself was originally to have been shot practically using synchronized high speed photosonic cameras, a dummy constructed by makeup supervisor Rob Bottin and live footage of actor Edward Norton. However, the filmmakers couldn't get the shot to look right, so at the last minute they decided to do the scene primarily CG instead of live. Ultimately, live footage of Edward Norton having 180psi of air shot into his mouth (to make his cheeks blow out) was used, but apart from the actual face, the only element of the shot which is real is the spurt of blood coming out of his mouth, everything else is CG. 

The final shot of the collapsing credit bank buildings was designed by Richard 'Dr.' Baily, who worked on the shot for over 14 months straight. According to director David Fincher, there are almost 4 million separately animated digital elements in the shot. 

In the closing seconds of the film after the camera pulls back from the exploding buildings, a single frame of male genitalia can be seen briefly like Brad Pitt's character added in his projectionist job. 

After the Narrator leaves Marla's apartment just before he meets Bob (who tries telling him about Fight Club) there is a graffiti written the wall to his right that says "I MYSELF I MYSELF I MYSELF I MYSELF". Parts of it can also be seen as the Narrator and Bob talk.