Set it on fire

Perhaps from a lit cigarette.

Old film stock was nitrate based...

Nitrate film base was the first transparent flexible plasticized base commercially available, thanks to celluloid developments by John Carbutt, Hannibal Goodwin, and Eastman Kodak in the 1880s. Eastman was the first to manufacture this for public sale, in 1889. Unfortunately, nitrate also had the drawback that it was extremely flammable (being essentially the same chemically as guncotton) and decomposed after several decades into a no less flammable gas (leaving the film sticky and goo-like) and ultimately into dust.

As this happened, the likelihood of auto-ignition increased even further. Projection booth fires were not uncommon in the early decades of cinema if a film managed to be exposed to too much heat while passing through the projector's film gate, and several incidents of this type resulted in audience deaths by flames, smoke, or the resulting stampede.

^Wikipedia

I have been a projectionist for over 20 years, so hopefully can help to answer your question. You don't say what period you are setting your story in as that has a bit of an impact on exactly how the damage might happen.

Nitrate film would have caught fire, from getting stuck in the gate of the projector and the heat from the Carbon Arcs. There were cut off devices designed into the projectors so that it would cut at the film at the top and bottom of the projector making sure only the film laced around the projector would actually burn.

More often than not, the reason that a film would get damaged while actually being projected is if a perforation on the edge of the film got damaged and caused the projector to lose a loop and get too tight or might cause the film to split in half as a result.

The other way a film might get damaged while being run on changeover is if one the projector it was on started to quickly and rather than slowly and would cause the film to snap.

In short, if the film had been on the circuit for a while, quite likely if it was an old cinema, then it is possible that the film had been damaged and that could get more damaged in the projector.

Lighting it on fire would be one option, but certainly a dramatic option! I'm not sure how much of a "splash" you'd be trying to make.

Other ways to ruin film come to mind:

1. Spill a drink (maybe a large soda) onto it.
2. Have the film reel fall apart with the film spiraling off into a pile on the floor (this happened frequently with the cheap plastic reels used with modern, polyester film).
3. He forgets to load the takeup reel, or it breaks, and the projectionist doesn't notice, resulting in a huge, tangled mess of film on the floor (it would be possible to recover from this, but painful).
4. Mis-threading the projector or otherwise getting the film stuck in it, resulting in a worst-case of a projector case jammed full of film.

Options if the film is set in a modern cinema running a repertory title (in this case, you'd be running a platter rather than changeover system):

1. The platter system spins out of control and throws the print off (yes, this used to happen).
2. A brain-wrap (being one of the more technical terms, it's every projectionist's worst nightmare).