Some readers suggested that I should change the coding of the widget, and leave out updated posts. I think that is not a very good idea, because an updated post could contain relevant new information. So I came up with an interesting trick.
Add the following styling definition to your blog's template:
.updateinfo { display:none; }
Now, whenever you update a post, at the beginning of the post insert update-information, using the following html:
<span class="updateinfo">UPDATE: Repaired some dead links. Content has not be changed.</span>
If you publish your post, the update info will not be displayed on your blogpage, but the feed, and therefor also the Recent Posts Widget, will show the update-text.