  The mass function of galaxy clusters is an important cosmological probe.
Differences in the selection method could potentially lead to biases when
determining the mass function. From the optical and X-ray data of the
XMM-Newton Follow-Up Survey, we obtained a sample of galaxy cluster candidates
using weak gravitational lensing, the optical Postman matched filter method,
and a search for extended X-ray sources. We developed our weak-lensing search
criteria by testing the performance of the aperture mass statistic on realistic
ray-tracing simulations matching our survey parameters and by comparing two
filter functions. We find that the dominant noise source for our survey is
shape noise at almost all significance levels and that spurious cluster
detections due to projections of large-scale structures are negligible, except
possibly for highly significantly detected peaks. Our full cluster catalog has
155 cluster candidates, 116 found with the Postman matched filter, 59 extended
X-ray sources, and 31 shear selected potential clusters. Most of these cluster
candidates were not previously known. The present catalog will be a solid
foundation for studying possible selection effects in either method.
