Power surges can affect movie theaters whether they use digital projector or film. The automation systems, essentially PLC-based machine controllers, can be shut down by power surges just as easily as computers and digital projectors can. The difference is that film projectors can be restarted much faster and easier. Just cycle the power and hit start. You might have to press a few extra buttons to cycle the automation to the right state but, once you have it running, it should just keep right on going from where it left off. A digital projector depends on its computer memory to play the digital movie file. If it loses power it can easily lose its place and it will have to be started over from the beginning. I do not believe that digital theater systems have the ability to fast-forward through the digital files. I believe it's all or nothing.
Remember, once a movie has stopped for any length of time, regardless of whether it is film or digital, you take a chance of pushing that presentation over into the next showtime slot. Suppose a movie starts at 12:00 noon and runs till 2:30 PM. The next show starts at 2:45 or 3:00 PM, depending on how the theater stacks its schedule. Therefore, if your projector goes down for longer than 15 or 30 minutes you are going to have to delay the next show. You will have a lobby full of impatient customers, wanting to sit down and see the movie they paid for.
So, regardless of whether you use film or digital projectors, a power surge might force you to cancel a show.
The smart theater owner will install power surge protection equipment in every theater. Unfortunately, there aren't a whole lot of theater owners who are that smart. Power surges do put a lot of theaters out of commission.
lxdude is on the right track. If theaters keep going the way they have been going, most of them will go the way of the dodo.
Crappy presentation, regardless of film or digital, and poor customer service will cause more and more customers to stay home and wait for the movie to come out on home video.
That is more of a threat to film than digital projector or 3-D will be.