Question: I made caramel on my induction cooktop. The temperature was correct, but the caramel texture is grainy, like all of the sugar didn't dissolve properly. Do I need a different thermometer? I used a Wilton clip-on stainless steel mercury thermometer. Or does the cooking time need to be adjusted?

The recipe I am using is: 1cup butter,2 1/4cup brown sugar, dash salt,1cup light corn syrup,1can sweetened condensed milk,1teaspoon vanilla. Melt butter in heavy 3 qt. saucepan. Add brown sugar and salt. Stir until thoroughly combined. Stir in corn syrup and mix well. Gradually add milk stirring constantly. Cook and stir over med. heat until candy reaches 245F remove from heat and stir in vanilla. Pour into 9x9 pan. Let set 24 hours. Cut into squares, wrap in wax paper. 

I am close to sea-level.

Answer: 
I noticed that you're stirring constantly. Generally with candy you want to stir as little as possible, since it causes sugar crystals to form in the syrup. In addition to making the candy grainier, they reduce the overall lifespan- even after the candy has cooled the (larger) crystals will continue to grow, causing the candy to slowly revert back into flavoured sugar.

Once the sugar is fully dissolved, you want to disturb it as little as possible. You will still have to do some stirring, otherwise the milk solids will burn. It'll help a bit to mix in the corn syrup at the same time as the sugar. Corn syrup is an *invert sugar*, meaning it gets in the way of crystallization and slows it down. If your caramel is still coming out grainy, try adding half a teaspoon of lemon juice. Your candy will be slightly gummier, but the acid in the lemon will inhibit crystallization and reduce the graininess.
Your thermometer should be fine, the graininess probably has more to do with technique than temperature. There's quite a bit of controversy as to when and how to stir and what to do about sugar crystals that form along the sides of the pan.

Just to be sure about your thermometer, test it with boiling water. If you're at or near sea-level the thermometer should read 100C or 212F. If your thermometer is fine, then we need to take a harder look at technique.

Edit: Looking at your recipe and considering your change in cooktop, I can only see a possible problem if the candy reaches 245F more quickly than you are used to. Try lowering the temp a bit at that stage so that it takes longer for the candy to reach 245F. It may take some getting used to, but induction should perfect for candy making.

It pretty much goes without saying, so I am assuming no considerable change in your ingredients.