One of the best investments I’ve made is buying a good tool for easily fixing small glaze runs. This technique can save mugs with small glaze flaws from ending up on the seconds shelf or in the rubbish.
A rotary tool is very useful for quickly removing small areas of glaze that have melted on pottery where you dont want them - most typically a run onto the foot of a pot.
I use a Dremel but there are plenty of other brands. The upfront cost is outweighed by the number of pieces that can be salvaged over the lifetime of the tool. Similar methods include diamond coated sandpaper or an axle grinder. I like the precision and speed of a rotary tool.
Rotary tools come with an overwhelming range of bit types. Over time I have found that all I need are a few sizes of silicon carbide bits and also a couple of diamond coated bits for the really tiny fine jobs. The silicon carbide heads are quire robust and last a long time whereas the diamond coated tend to wear out fast.
The technique will throw up small amounts of fine dust and create an inhalation risk. Shards of glaze often fly off. Wear a face mask, safety glasses, and thick gloves. It helps to dab the surface you are working on with water to reduce the amount of dust rising. I prefer to work outdoors (using a waterproof outdoors extension cord) so that the dust doesn’t settle in my studio.
Take some time to follow the operating instructions for your rotary tool and then get cracking using it to grind off any flaws. Work gently at first to guage how much material is coming away and then shape and finesse the repair.
Here are three mugs with different flaws that I have recently repaired with the rotary tool.