This is a known and reported fault that seemed to have started after Wiki updated the appearance and features earlier this year. Apple and Wiki have the fault logged but it seems to be in Wiki's court at the moment. If you need too use it rather than direct to Wiki, then there is a workround that switches off the new features in Wiki. This seems to work for most people:
1. From your browser, go to Wikipedia's main page and log in. Use the "remember me" feature. (Register if needed)
2. In the upper right corner, click on "New Features."
3. Under "Take Me Back" section found in the lower middle of the next page, click the "click here" indicating you would like to turn off the new features.
4. Fill out their little survey asking why you want to turn them off and update.
That's it. The next time you access dictionary.app, the scroll bars should be working under the Wikipedia section.