How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?

Per Korzybski, I'd say that whatever you say matter is, it is not. Modeling matter as coming in discrete configurations works quite well, though we've seen that there are exceptions where the discrete configurations can be reconfigured if properly physically perturbed. I wouldn't be surprised if there are tons more stable configurations than we've seen or created so far, and even some that no longer model well as "discrete".