Have you ever spent a lot of time on a piece, then opened the glaze firing to find out that the glaze ran right down to the kiln shelf? It may be worth trying to grind the glaze off to save the piece (or at least have it has a functional second).
First, cut off most of the glaze with a cutting disc and rotary tool. Go slow and let the tool do the work. Don't apply too much pressure and try not to bend the cutting disc. Always wear eye protection when using a rotary tool.
Next, start grinding the glaze down with a coarse grinding wheel or grinding attachment on a rotary tool. Slowly grind down the glaze until the foot looks uniform in shape again. After the rough grind, switch to a fine grit sand paper to polish off any sharp edges.
Here's a quick video of grinding off a glaze run from the foot of the pot.
Another problem you may run into is a wobbly or rocking pot. Sometimes this happens because a wonky kiln shelf or kiln wash kept the pot from shrinking properly during glaze firing.
The only way to get a wobbly pot to sit flat is by using a large diamond sanding disc. Many people don't have this, but here is a little video demo on how to do it anyway.