What constitutes measuring in the double slit experiment? In the double slit experiment attempting to measure which slit the particle passed through causes the wave function to collapse.
According to the question: What is the quantum mechanical definition of a measurement?

Until we have an accepted solution of the Measurement Problem there is no definitive definition of quantum measurement, since we don't know exactly what happens at measurement.

And:

The many-worlds interpretation defines measurement as any physical procedure in which the observer gets entangled with a quantum system.

To me, the most obviously arising avenue of investigation would be to narrow down on precisely what does or doesn't cause the wave function to collapse.
Have physicists extensively experimented with what conditions cause it to collapse? Do you have to be taking a measurement to make it collapse or will any interaction cause it to collapse?
For example, what if you measure it with an apparatus that then destroys the data gathered without allowing the data to exit a faraday cage, so that it is impossible for any information to ever be accessible to the outside universe? Then what ever the answer, one might invent even more obscure hypothetical circumstance to test...
Has this avenue been explored?
 A: What causes interference pattern to vanish? Suppose we send a particle through two slits. Then you will see an interference pattern.
Now, suppose there is some asymmetry in the two slots, so that somewhere in the universe (not necessarily accessible to the experimenter) there is some information telling which of the two slits the particle went through. Then the interference pattern vanishes.
There might be incomplete information that only gives us a probabilistic guess as to which slit the particle went through. In this case, the interference pattern is dimmer, but it doesn't go away completely. 
Finally, to make things even more complicated, there is a very clever experiment that shows that, after we make a measurement $M_1$ that gives us some information (we keep the results of this measurement in quantum superposition) telling us that which slit the particles went through, we can make a second measurement $M_2$ on this information we kept which destroys it. What happens here is if we just look at the results of $M_1$, the interference pattern is gone. But, conditioned on the result of the measurement $M_2$, the interference pattern reappears. This is called the quantum eraser experiment.
So does the wave function collapse after measurement $M_1$? No, it can't because we can restore the interference pattern with measurement $M_2$. But it's not the experimenter looking at the results of $M_1$ that collapses the wave function, because we can just throw the results of measurement $M_1$ away, rather than remeasuring the outcome with measurement $M_2$. If we do this, the interference pattern is gone forever, without the experimenter ever learning anything about the measurement.
I would stop worrying about what makes the wave function collapse, and start worrying about what causes the interference pattern to go away. Nobody knows when the wave function collapses. And some of the people who believe in the many-worlds interpretation of QM claim that the wave function never collapses; what happens instead is that the experimenter gets entangled with the outcome of the measurement.
A: What makes the wave function collapse is not the fact that anyone sees the result of the observation, or that the information is accessible to an observer, it is the interaction between the macroscopic apparatus and the microscopic quantum system. I don’t understand how one could think that physics would work in such a exoteric way such as the one proposed, where the state of a system would only be determined if someone checked the results of an experiment, or only if these results were somehow available. It is clear that what changes the state of the quantum system being measured is the interaction with apparatus. You can make a machine that interacts with the passing particles in the double-slit experiment that works just like the one where you try to measure which slit it went through, but this machine does not record any data, and in this case the interference pattern would be destroyed just like in the other case. 
A: In the specific double slit situation, measuring which slit a particle goes through changes the boundary conditions of the quantum mechanical solution, which is what gives the interference pattern as an accumulated probability distribution. A different wave function is generated by the change in the boundary conditions.
Here is how the probability distribution predicted by the wave function in the experiment "electron scattering off double slits of specific width, distance and medium (vacuum)"

The way that the "which way" detection was attempted in this particular experiment shows the boundary condition changes clearly:


With a filter over the right slit, electrons are more likely to undergo inelastic scattering and act like a spherical wave. Electrons passing through an uncovered slit are more likely to undergo elastic scattering and act like a cylindrical wave. The two different waves do not have a phase correlation and so, even if an electron passed through both slits, it could not create an interference pattern.

Italics mine.
There is no longer the same "medium" in each slit, which changes the wavefunctions. It is worth reading the link.

Although the electrons (which were shot one by one) could still pass through the filtered slit, the filter caused more of the electrons to undergo inelastic scattering rather than elastic scattering. As the physicists explained, an electron undergoing inelastic scattering is localized at the covered slit, and acts like a spherical wave after passing through the slit. In contrast, an electron passing through the unfiltered slit is more likely to undergo elastic scattering, and act like a cylindrical wave after passing through that slit. The spherical wave and cylindrical wave do not have any phase correlation, and so even if an electron has a probability to pass through both slits, the two different waves that come out cannot create an interference pattern on the wall behind them.

Italics mine, it is a different wave function.
This should be a clear demonstration that the quantum mechanical probability interference pattern depends on the boundary conditions, and any detector/interaction  at the slits will change them and thus give a different incoherent wave function and so the interference pattern in the accumulation will be lost.
