Double slit experiment paradox Two observers – A & B - conduct a single double slit experiment and watch the same detector screen for the appearance of an interference pattern.
A separate detector records which slit each particle passes through, but the data from this detector is only available to observer A. 
As I understand it the wave function should therefore collapse for observer A, but not for observer B. Observer A will therefore not see an interference pattern on the detector screen, but observer B will.
How can this be when both observers are watching the same detector screen during the same experiment?
 A: You are wrong, but understandably so given the ridiculous way in which quantum measurement is commonly discussed. A measurement is an interaction that makes a record of the value of some observable. If such an interaction happens during an interference experiment, the interference doesn't take place. What matters is whether there is a record, not whether some observer has looked at it. All this is a consequence of unitary evolution:
http://arxiv.org/abs/1212.3245,
the collapse postulate is entirely unnecessary.
A: All measurements come from interactions. In our macroscopic world, our intuition is that we can observe things without affecting them, but this is not true at quantum scales. In order for that measurement at the slit to happen, the photon has to interact with something — an electron, say — which couples the state of the photon to the state of the detector, which in turn can be read. This coupling destroys the coherence between the two paths through the slits so that they don't interfere.
The idea of wavefunction collapse is a simplification that we use when we are modelling only part of the total system with our equations. For example, it's common to write down a Scrödinger equation for a single particle, but not include a representation for what detects the particle. Such models work fine as long as one remembers to collapse the wavefunction after a measurement event. It's just a model, though, it doesn't represent all of reality.
In general, remember that quantum mechanics is physics, not philosophy. "Observers" get conflated with conscious beings a lot in popular conversation, but that is not how best to understand them. When physicists speak of an abstract observer, it's really a label in a thought experiment to group together certain physical interactions. In the case of wavefunction collapse, the wavefunction is the simplified representation of a small physical system, and the observer is whatever breaks the boundary between the larger world and that system. In this case this is the slit detector, as @Jimnosperm describes.
