booster17 asked for the letter B...
"Bad Note for a Heart" - Straitjacket Fits. Probably cost more to record than the rest of the songs in this bunch put together (and the same probably goes for the video). First time I ever saw Suede on TV I thought "that bloke wants to be Shayne Carter when he grows up".
"Basket Case" - The Terminals. Back when the Terminals coalesced into what seems to be their current line-up, one could have expected the combination of the original Terminals and Brian Crook, fresh from somewhat acidic country and western band the Renderers, to have produced something mid-way between the two sounds. One could have been very wrong. Their next recording - "Touch" - sounded like the result of a high-speed motorway collision between a rock group and a country and western group: fragments of music scattered all over the soundscape. This song is one of the roughest and most chaotic things of theirs that I've ever heard. More information on the album here.
"Beatnik" - The Clean. This is what passed for a big budget video in early 1980s Dunedin. This song came off a record that had "BRING BACK MONO!" written proudly on the back (they didn't bother with typesetting on their record covers).
"Big Bang Theory" - Able Tasmans. Odd but good... which fairly much sums up the band, actually.
"Brain that Wouldn't Die" - Tall Dwarfs. I get audio flashbacks of this song whenever a couple of the Usual Suspects at work use the ping pong table in the cafeteria.
... and grygon asked for the letter M...
"Mastery" - The Bats. Any list of songs is better with a song by the Bats in it. If they look (and sound) vaguely familiar, it's because it is they who were caricatured in (and provided the soundtrack for) the vaguely Munsters looking video I linked to a few weeks back.
"Maybe" - Split Enz. A terrible recording of a great song. (I didn't even know home video existed in 1975 - and it mustn't have been much good; there's some serious faults in the recording at about 1:25). Believe it or not, one of the usual suspects running around like maniacs on that video is now the public face of the Australasian Performing Rights Authority, and one of the singers (the higher and less nasal one) co-wrote "The Weather with You".
"Midnight" - Hammond Gamble. Musically this is a bit of a change of pace, I know... this guy puts on a good show live (I saw him play at the Civic Theatre a couple of years back). This particular video is live in Oamaru, of all places.
"Mir" - The Bats. Partly because two videos of the Bats are better than one, and partly because most of the groups I like seem to be boycotting the letter "M" on general principle.
"Mr. Moon" - Headless Chickens. As with anything the Chooks do, this one is rather odd. (I'd rather have linked to "Magnet", but they don't seem to have ever made a video of it - or if they did, it isn't on You Tube).
And if anyone wants me to give them a letter, there's the original set of instructions way down here.