How did he screw up by pleading 'no contest'? What were his other options?

Remember that he was in possession of a CII substance. That's plain and clear. There was no way out of it.

I don't think the option of pleading not-guilty, asking for a jury trial, and crossing your fingers hoping for a hung jury or jury nullification would have been wise.

I also see why the judge made him notify his employer, considering he was a bonded stock broker.

After that, the "process" took over.