At low speeds, my blender has a grinding, "bumping" sound. When I progressively turn up the variable speed knob, the motor revs way up and then slows way down again until I get to the highest speeds and it stays at a fast speed. The grinding sound is always there at low speeds, even with the drive socket removed.

Replace the potentiometer with a better one. Do not use the CHEAP PIECE OF CR@P that comes with the blender. For what they charge for these machines, they should be using MUCH better components. I used part RV4N502C-ND from Digi-key as described by another poster for a different model. The knob didn't fit, so I also used Mouser part #5164-1500 knob, which look exactly the same.

This problem sounds like failure of the Variable Speed Potentiometer component. Here is the most helpful Fixya article so far: http://www.fixya.com/support/t6032529-need_replace_speed_control
I have the same problem right now and don't want to pay ridiculously high prices for a small electronic component.
So far, this is as far as I've gotten in researching replacement parts:Vitamix Part #015955
Partstown sells #15955 for $23.39 on their website but I found out they charge $15 for shipping -- for a one-ounce piece of electronics. I won't pay to be ripped off on shipping so I won't buy one from Partstown until I've exhausted less-expensive suppliers. Here is the product at Partstown: http://www.partstown.com/vita_mix/vm15955
Another Fixya contributor, Robert Sadler, said he was going to try a generic potentiometer from Mouser.com. His descriptions are kind of vague for me. I'm not an electronics expert so I'm not very confident I can interperet his description:
"If you are comfortable with soldering, you can get a replacement part at Mouser.com. The pot is a 5k "slimline" made by Bourns, however looking inside the cover it looks like most pots would fit. I ordered one for a bit over $5 and will update when I get it with how it worked. You would just have to solder the existing wires to it." -Robert Sadler
I have no problem soldering the existing wires onto a new component but I don't really know what would be an appropriate potentiometer to buy as a replacement from an electronics supplier. In addition, Mouser's website seems to sell potentiometers only in bulk quantities of 5, 6, 12, or 45 items at a time. I just want one.
If anyone knows how to interpret Robert Sadler's comments, or has actually done this repair, please post below. I'm sure quite a few people would benefit from a high-quality repair at a low component cost.