Is there any way other than watching a movie or trusting IMDB to see the credits (such as closing credits) of any movie?
I would assume that the industry itself must store this kind of data somewhere since this is a practical necessity (e.g. people need to be paid residuals,...). There is for instance the Motion Picture Credits Database:
Every year, as part of the Academy Awards process, the Academy gathers credits from films hoping to qualify for awards. To these credits, compiled and verified by the film's producer or distributor, we add credits from other films released in Los Angeles County, using research materials from the Academy's Margaret Herrick Library.
In addition to personal credits, MPC records index production and releasing companies, MPAA ratings, running times, Los Angeles release dates, color, language, source authors and source material, all of which are searchable.
The credits in the MPC database were originally collected and printed in the Academy publication Annual Index to Motion Picture Credits. The Index started in 1934 as the Screen Achievement Records Bulletin, when the Writers Branch of the Academy began publishing a bulletin of screen authorship records.
... and the Official Screen Credits for Academy Awards Consideration (same page, I'm not going to copy-paste the entire description).
This page mentions several databases, some are only available to UCB users.