Simply put, the initial "grapes" you see are not grapes, but the buds of grape flowers. The "starburst" is the actual flower, which will turn into a grape. In other words, nothing is wrong with that picture, your plant is happy! Look at the images...

Here is a link that might be useful: Grape Flowers

Thanks for educating me. All this time I thought this was a problem. From the images shown mine don't develop as much. Anything I should be doing to enhance the clusters? Thanks again

I have the same thing happing to my grapes. I thought I had some kind fungus or something.

Since I don't know what conditions your grape is growing in, I would recommend the following: Full sun, water, fertilizer, and good air circulation. I don't know what to fertilize grapes with, but I would think that you would want less nitrogen than phosphorus and potassium, fert. bags are have three numbers: N-P-K (nitrogen, phosphorus, and potassium), look for a lower first number. I would recommend using an organic fertilizer as well, because you are less likely to burn the plant if you overdo it.
I think the flower size looks fine. Have the grapes been unusually small in the previous years?

not small, but certainly not the full bunches that one would expect.

not small, but certainly not the full bunches that one would expect.