If you plan to open the speedometer, download the 27 page PDF by Anthony Rhodes on Smiths and Jaeger speedometers.  
//obswww.unige.ch/~wildif/cars/docs/Smith-jaeger_speedo_repair.pdf

Read it through first before you get started.  Take pictures as you take things apart.  Make sketches of details.  And perhaps most importantly, carry out your work on a white sheet in a well lit area to minimize the chance of losing parts.

Awesome, thanks everyone for the information, I will remove the speedo this weekend and see if I can crack it open. I hope there is not too much damage at this point. 

Others have already explained what's going on.  Dirt also collects around the needle bearing that supports the far end of the spindle the needle is on.

I will add that with the drag as bad as you describe, I would disconnect the cable from the gauge before any permanent damage happens (assuming it hasn't yet).  When the drag gets bad enough to drive the needle around to where it is pointing down... it's only a short amount of time before the needle is driven all the way around and the hairspring that returns it to zero gets twisted into a knot.  If the needle is not returning to the stop peg at zero MPH, then damage has already occurred.  

There are numerous places that will be able to rebuild your gauge when you are ready.  Opening them up and servicing them at home isn't for everyone.

The speedo works on a magnetic drive using two plates inside the speedo unit.  One is driven by the speedo cable and the other is dragged around, against a spring, by the magnetic force between the plates.  Dust and grunge can collect between the plates making it more of a direct drive (the plates are kinda stuck together). (The speedo is calibrated by adjusting the distance between the plates.)

One way to clean this gap out is to take a thin hacksaw blade and cut it in half (both directions).  Lose the teeth and trim the back bit down to about 4 (ish) inches long.  Now carefully wipe your newly manufactured stiletto around the gap between the plates (poke tip into the centre and wipe the tip outwards).

With the gap clean the speedo may (where's the crossed fingers emoji  begin to work properly again.... 

Cheers, Ian

remove the speedo  and open it up, or just swap another one in there.  Possible needle or shaft not fitting tight.

Good question - sorry I didnt give more specific information 

A bit of both. The needle will rotate beyond the ~140kph indicated maximum to hover over the fuel gauge, pointed straight down. Also I have noticed that the needle will occasionally not return to zero when coming to a stop in a parking lot, or at a red light. 

Do you mean the needle is pointed straight up or straight down?  Does the needle return to the stop position against the stop pin or does it stop at a hovering position higher than zero?

Hey guys, Im hoping that someone can give me some place to start troubleshooting a problem I am having. 

I just picked up at '72 Austin 1000 which had the speedo cable broken. I replaced it, however after doing so the speedo needle moves, but it stays fixed waaaayyy too high. It usually hovers right over the fuel level.

Can anyone give me a point in the right direction? I dont really want to go straight to replacing the speedo, however I cant really think of anything else at this point.  

Cheers!