With TV, radio, film and other forms of mass media will accents and dialects slowly die out or transform until there is just one national/non-regional dialect?

Certainly the trend in many countries is for dialects to die out, particularly countries with a strong centralising tendency in culture and education. Greece and France are very good examples of this. Even in England, what survives is more accents with some variant vocabulary than the full-fledged dialects of two centuries ago.

Countries that have not as longstanding a centralising tradition preserve their dialects better: Germany and Italy are the best examples in Europe, and it is no coincidence that they only became unified countries in the 19th century.

There are centrifugal pressures that preserve linguistic variation: people don’t really *want* to all sound the same. The US for example has a Mid-Western standard, but it also has plenty of emerging vowel shifts hither and thither. (See Are we losing the regional dialects in the U.S.?) But mass media, combined with universal literacy, and population mobility all mean that there is more pressure on people to at least use mutually intelligible variants of the same national language. (The first blow to dialect diversity in Greece was not mass media; the media was in an archaic variant of the language that most people only semi-comprehended. It was universal conscription.)

That means that it’s harder now in a first world country for dialects to drift as far apart as they have done in Germany, and to have significant grammatical differences as well as phonetic and lexical differences. And peoples’ desire to speak differently can be satisfied by a different accent as much as by a different grammar. So the centrifugal pressure on standard languages is less effective now than it used to be.