A colleague's CV is taking credit for service that I did, and now we're both on the shortlist for a job. Is there anything that I can do?
I would just ignore it. I doubt that anyone will even notice unless they look at the two CVs side-by-side, and even then, they will probably just assume that the two of you worked on the redesign together. They wouldn't doubt your honesty (nor the other editor's). So I don't think this really disadvantages you.
It might be a slight unfair advantage for the other editor, but I think it's minuscule. In hiring decisions, things like professional service get a very low weight. The fact that you were an editor is perhaps somewhat helpful, if the journal is recognized as publishing good research, but what you actually did as editor is too minor a point. The fact that you can redesign a journal may speak to your graphic design skills, but academic jobs don't care about that - they care about your research and teaching (in some combination). In fact, I'm not sure it is wise to emphasize it in application materials or interviews - people might think that tinkering with your journal could be a distraction from actually doing research.
If the topic of the redesign comes up at the interview, just describe honestly what you did. You don't need to get into what your co-editor did or didn't do.
I doubt that you will be asked specifically about the fact that both of you are claiming credit (for one thing, it would reveal that the other editor is also a candidate for the job, which would normally not be shared with other candidates). But if so, I would say something like "As co-editors, we share the responsibility for what happens to the journal on our watch. But on this particular project, I took the lead."
The situation sounds unfortunate. I don't know the details of what you and the other person claim. However, I think that someone looking at both of your applications will not immediately suspect dishonesty.
It's quite normal for people to take credit for joint work. If the other person is listed as a co-editor (or co-author if the work is a paper), they generally have the right to claim credit. It's only really problematic in situations like yours where the contribution was entirely unequal. Ideally this situation would have been resolved in advance by removing them as a co-editor.
There is not too much you can do about it. Trying to raise a dispute or do anything to criticize the other candidate will make you look bad. However, there are two things that you can do in general:
Have your references explain your contribution. This requires you to have one of your references be knowledgeable about the situation, which may not be possible in your sitation.
Be prepared to discuss the situation in your application or in the interview. If you can give a more detailed and confident explanation of what you did, then it will be apparent that you were more involved. However, you should be careful to avoid disparaging others. So prepare diplomatic answers. Talk positively about your work, not negatively about others.
I agree with @NateEldredge for the most part.
A piece of advice which is "wisdom in hindsight" for OP, but may be relevant to others:
If you have a bit of your CV, or your work, that you're particularly proud of as an experience (as opposed to a paper with your name on it) - either manipulate your environment to make some written acknowledgement of what had happened (e.g. in OP's case - publisher sends him a thank-you letter with fancy letterhead), or write about the process ex-post-facto in a blog. It shouldn't be self-laudatory, but if you're genuine enough, and link to people you worked with, and present what things were like before and after, and maybe describe some kind of lesson learned or even extol and praise others who were involved - that makes it clear that you really did do that.
Now, the thank-you letter is not something you can put in your CV, but you could theoretically use that if asked about who-did-what. The blog post is something you can link to from your CV, and that really nails down the who-can-take-credit question. Of course, as a commenter suggests, don't expect the people reading your CV to actually read it; they'll just note it's there.