MediaWiki is very good, but for programming tasks editing it via the web is not very handy since WYSIWYG is very limited. Pressing 'edit' + 'publish' on any small change and waiting for page loading is kind of annoying. I have seen a lot of desktop wikis (personal wikis) that are free from such problems. The best example is WikidPad that has a usage pattern of 'focus, edit wiki in-place, minimize'.
Does a desktop application exists that can connect to MediaWiki and allows to view and edit it via a rich WYSIWYG editor? Any hints are welcomed.
Not really. For an explanation and a list of imperfect options, read this page.
However, you might not need a WYSIWYG editor in order to make many quick edits to a wiki. It is possible to download the wikitext of a page, edit it locally, and submit the changes. There are scripts (called bots) available which do this. One example is pywikipediabot's "editarticle.py" script. You might also want to take a look at AutoWikiBrowser.