Q:

Why was Mundungus banned from the Hog's Head?

In Order of the Phoenix while the trio were in the Hogs Head for the first time plotting the start of Dumbledore's Army, it transpires that ol' Dung was lurking in the pub in a disguise, having been banned 20 years previously according to Sirius. 
Firstly, why was he banned? this could possibly be the tight spot that Albus had helped Dung with in the first place that made him loyal to Albus.  
And secondly, how is it that he is then speaking to Aberforth in Halfblood Prince? (assuming the ban was for something rather unforgivable, 20 years is a long time?) 
They both could have been in the Order by then, but unlikely given Aberforth's attitude in Deathly Hallows once the trio arrive in Hogsmeade looking for the tiara.  We learn now that a lot of trafficking goes on through the Hogs Head so maybe Dung was trading with Aberforth, Sirius' mirror and various other Black artifacts, he just was not allowed in the pub. 
Anyone with something in canon or more plausible?

A:

why was he banned?
I'm not able to find any canon data on that, either book text search or interviews transcripts.

how is it that he is then speaking to Aberforth in Halfblood Prince?
In HBP, he's speaking to Aberforth, NOT being inside Hog's Head. The topic was selling stuff he stole from Sirius' place:

Nikki: How did sirius twoway mirror end up with aberforth or is it another twoway mirror?
  J.K. Rowling: You see Aberforth meeting Mundungus in Hogsmeade. That was the occasion on which Dung, who had taken Sirius’s mirror from Grimmauld Place, sold it to Aberforth.
  (src: J.K. Rowling Interview / The Deathly Hallows Web Chat / July 2007)

As a note - this was important since one of the things sold was the 2-way mirror that Harry used to request help when they were imprisoned at Malfoy's in DH.
So, he was banned from the pub (probably, to avoid causing Aberforth's establishment further trouble), but doesn't mean Aberforth won't talk/do business with him otherwise.

