After three years of learning German, I have a reasonable understanding of, and ability to converse in, (Austrian) Standard German. But, living in Salzburg, I am still really struggling to understand even basic things when spoken in local dialects. I don't watch much TV, but have recently discovered that Bavarian TV has series like 'Dahoam is Dahoam' which I guess with a lot of subtitle-assisted viewing I could help to train my ears to understand that dialect. Are there any shows on Austrian TV where I could regularly hear local dialects spoken and try to tune in to them a bit better? Unfortunately the 'just hang out with locals and chat' approach isn't working for me, either I'm left sitting there understanding nothing, or everyone switches to English for my benefit.
Try "Vier Frauen und ein Todesfall" which has some rural dialects in them. Among the older ones is the crime series "Stockinger" which is set in rural Salzburg.
For the specific Viennese dialect, "Kaisermühlen Blues" is a classic as well as its crime version "Trautmann" which are almost completely in Viennese dialect. And "Kottan ermittelt" for fans of the 70s.
The answers of alex2006 and Fred Bob are both correct. I just want to add something:
About Austrian TV-shows:
The ORF (Österreichischer Rundfunk) (English: Austrian Broadcasting Corporation) is producing many movies and TV-Series, and most of them (not all) use Austrian colloquial speech. Also if you google for "österreichischer Film" you will find lots of movies in Austrian colloquial speech. Most of them are also available with subtitles.
But there is no permanent daily or weekly TV-show in Austrian colloquial speech or dialect.
About Austrian colloquial speech and Dialects spoken in Austria:
There is a difference between Austrian Standard German, colloquial Speech and dialects.
As Fred Bob already said: Dialects use a different grammar, different vocabulary and different pronunciation. For example, the dialect of the south-east of Styria, near Graz, where I grew up, has no genitive case and no plusquamperfect (like most of Bavarian dialects).
But even more important: Dialects differ strongly from region to region. Every state (Bundesland) has its own dialect, and even within the states there are manny different shades. So, there is nothing like "the Austrian Dialect". Ich you move from Salzburg to Eisenstadt, there is a Dialect of Salzburg, A Dialect of Linz, one of St. Pölten (where I live now), many different Dialects in Vienna and the dialect of Eisenstadt. And many grades in between in smaller towns and villages.
So, what producers of TV-series do, is this: They use a dialect with many speakers (most often a Viennese middle-class-dialect), and then they replace vocabulary, that is too specific for that region with words that are known in a wider area. This gives a language, that will be understood in whole Austria, is still close to dialect, but is not standard German.
On Wikipedia there is a list of List of Austrian television series. And the Producer Hoanzl offers DVDs of Austrian Movies, Music and Austrian Kabarett shows (Austrian Kabarett is very different from German Comedy, and it is almost always in Dialect. And it is not cabaret!)
Not a direct answer.
The difficulty with German dialects is that you tend to approach them as if they were just differently pronounced Standard German, which they aren't. They have their own grammar and vocabulary, so the best approach, if you want to learn them quickly, is to get a textbook that teaches you the dialect you want to learn.
Search for "österreichisch" on Amazon.de and look at th descriptions and reviews. I don't know any of the books, so cannot recommend one.
You can certainly learn Austrian from tv and radio, but it will take some time, and using a textbook (and maybe a list of the most common words) will help you make progress much faster.
Besides tv shows, I can also recommend Austian radio and especially musicians that sing in Austrian dialect, such as Wolfgang Ambros, Georg Danzer, Rainhard Fendrich, etc. Wikipedia has a couple of list pages on Austrian singers, musicians, bands, etc. Listen on YouTube.