I have seen a dive operator rent out a computer that has just been used by another diver to a diver about to do his first dive of the day!
Personally if all I have is my dive watch then I rent everything else and use tables.
Assuming the computer wasn't reset between users which would be best, all this does is limit the second divers bottom time. It makes the second divers profile more conservative.
It's the other way around that you have to worry about from a DCS perspective - "I lost my computer on dive 1, may I use a fresh computer for dive 2?" That's a no no since the fresh computer doesn't know the diver already has some nitrogen loading.