Although my title seems to contradict itself slightly, are there any instances in which a German dialect has a kind of “standardised” orthography? While living in Austria, I spoke a heavy Vorarlberg dialect and noticed that there were often phrases from the language which had somehow been written with a standard orthography (especially in shops like Sutterlüty)!
No government-official standards exist in Germany to the best of my knowledge, unlike the official orthography rules. As far as I know, Luxemburg has a standardised orthography for Lëtzebuergesch which is typically considered a dialect of German. (I cannot really speak for Switzerland, Austria, Belgium, South Tyrol or Liechtenstein)
Within Germany and concerning its many dialects, it is impossible for a one-size-fits-all solution: Different dialects have pretty different phonemes to a certain extent.
Taking Bavarian and a word like Wasser, depending on the system you use you may arrive at the spelling Wassa, Wåssa, Wossa or any of these with a final -er. Different writers will prefer different spellings: the Bavarian Wikipedia uses Wossa while I would write Wåssa or Wasser. Standardising would either require an uncommon (for German keyboards) diacritic or an orthography that some feel over- or underdoes it. It is very hard to accomodate. On the other hand, some words such as Kasspatzn are clear in that they can only be written sensibly in one way.
The flip side is that many dialect speakers will usually guess correctly which word is meant even if they don’t initially recognise it.
I know of at least three orthographies for German dialects: