QGIS includes topology editing tools, so you can repair the un-dissolved municipalities polygons by doing a topology edit on them all at once.
- Set a Search radius for the maximum gap you would like to fix
- Set a maximum Snapping distance for vertices to be snapped
- Select all the polygons
- Move them from 0,0 to 0,0
(allowing them to search and snap and fix topology errors)
Now perform the dissolve as before on the clean municipalities set and review the results for fragments.
If any fragments exist, measure the sliver width then go back and repeat the process beginning with an original set, adjusting the Snapping distance based on the sliver width...lather, rinse, repeat as necessary.
EDIT: I was asked where to find examples of such editing.