I am writing a paper, and would like to use some GPL-licensed material I found on the internet; for instance, an image. The GPL requires any work using GPL content to be GPL licensed itself. To my understanding, using GPL content would make it impossible to transfer the copyright to the publisher, and therefore unacceptable for most research papers. It is correct?
This would be a problem if you used GPL-licensed piece of software and decided to release your derived program in a GPL-incompatible way.
Other than this, you should be fine. The point of GPL is that if you improve the source code, then your improvements (in case you want to make them public) must also be licensed under GPL.
Certainly GPL does not "infect" your publications - you can e.g. cite a piece of code released under GPL, without any problems. (And you can write your paper on a Linux machine, thus running GPL'ed OS :-))