Is there a scale for measuring wobbliness?

I was going to suggest a field sobriety test before I saw the rest of your question. If there was such a scale, I am sure Humpty-Dumpty would still be with us today!

Yes it's the Farquharson scale.

Things that move a little are only minorly Farquharsonal, anything that wobbles so much it breaks is said to be completely Farquharsoned.

It's similar to the scale used to measure earth tremors, but is called the RECTUM SCALE.
You may hear people refer to it just post a large "wobble" (as we call them in the trade) and the resultant gravitational effect upon said items - "blimey, that rectum!"

Wobble is defined as the variation from the vertical of a rotating shaft or basket. The USP defines the maximum acceptable wobble as ±0.5mm.

Wobble is measured on a paddle, just above the position of the blade. With a basket it should be measured on the rim of the basket. This highlights the need for correct handling and storage of baskets and shafts. Bent baskets or worn clips are not acceptable.

The QLA wobble meter is very simple to use. It uses a special vessel cover that fits inside the top of the vessel. This provides a static anchor point for the meter. (External devices offered by other companies tend to be hard to keep in position).

The wobble meter is firmly attached to this cover. The gauge is placed against the shaft or basket that is then rotated at a slow speed. Deviation from the vertical is displayed on the easy-to-read dial. The test is repeated in each vessel position.

http://www.labhut.com/products/dissolution_accs/validation/wobble_meter.php copy