Delayed Choice experiment:
For example, consider a delayed-choice thought experiment in which a photon can take two paths simultaneously. If the experimenter wants, he can "determine which path the photon took" by letting it hit a pair of detectors; it will register in only one detector, randomly chosen, as far as he can tell. The paths are laid out in such a way that in order for it to hit a detector, it must have taken the corresponding path. Taking the other path would cause it to sail past that detector and into the other one.
Or, he can insert a 'beamsplitter' (BS2; conceptually, a half-silvered mirror) to recombine the beams, in a way that results in the photon always going to the rightmost detector due to wave interference - in which case it must have taken both paths. He can choose whether to insert the mirror just before the photon reaches the detectors, after most of the paths would have already occurred!
Sure - if you think about it the wrong way.
In terms of wave mechanics (which is the MWI), the photon took both paths in all cases. If the beam recombiner is not present, the photon becomes entangled with the detectors - that is, becomes correlated with their degrees of freedom in configuration space. In one 'branch' of the wavefunction, one detector clicked; in the other, the other did. There is no 'delayed choice' mystery. [There is only the standard question for the MWI of what explains the appearance of probabilities - the old Born Rule problem.]
Most of the mysterious aspects of QM make a lot more sense when viewed as just wave mechanics in configuation space. But it's hard (impossible?) to find an introductory treatment of QM that even mentions configuration space. An advanced treatment of QM is unlikely to be much better - the equations will be there, but with little explanation.
The next post will be a basic glossary of common QM terms such as 'entangled'. Then I should be getting on to start discussing MWIs in more detail.