Hi Maximilian, I have a few examples. I am not sure whether they are of the kind you are interested in, but I thought I mention them nevertheless.
Bell has a paper [Intl.J.Quant.Chem. 14 (1980) 155; reprinted in “Speakable and unspeakable in quantum mechanics” p. 111] on how Bohmian mechanics answers the question of whether a delayed-choice experiment involves retrocausation.
There is quite some literature on how Bohmian mechanics helps for scattering theory; here is a selection of references:
M. Daumer et al., J. Stat. Phys. 88 (1997) 967, arXiv:quant-ph/9512016.
D. Durr et al., Lett. Math. Phys. 93 (2010) 253, arXiv:1002.0984.
T. Norsen, Am. J. Phys. 82 (2014) 337, arXiv:1305.1280.
People have also used Bohmian mechanics to consider the questions of how long a tunneling particle remains inside the barrier and whether it moves there faster than light. Two references:
C.R. Leavens, in: J.T. Cushing, A. Fine, S. Goldstein (eds.), Bohmian Mechanics and Quantum Theory: An Appraisal (Kluwer, Dordrecht, 1996).
And, again, T. Norsen, Am. J. Phys. 82 (2014) 337, arXiv:1305.1280.
I personally found the Bohmian picture useful for studying the probability distribution of the time at which a detector clicks. I hope to write a paper about it one day.
I have used Bohmian mechanics in the analysis of systems in thermal equilibrium, which has led to the use of the so-called GAP measure, a probability distribution over wave functions appropriate in thermal equilibrium [S. Goldstein et al., J. Stat. Phys. 125 (2006) 1193, arXiv:quant-ph/0309021]. The GAP measure was introduced without Bohmian mechanics (and termed “scrooge measure”) by R. Jozsa et al., Phys. Rev. A 49 (1994) 668, but no connection to thermal equilibrium was made.
I am presently working on a paper with S. Goldstein and W. Struyve using Bohmian mechanics to evaluate the question whether Boltzmann brains will appear numerously in the late universe, assuming the late universe will be in the Bunch-Davies state on a de Sitter space-time.