Regarding anesthetic risks, what specifically should DM patients tell an anesthesiologist before surgery?

Perioperative complication is increased in patients with DM.  All drugs, including sedatives, induction drugs, anesthetics, neuromuscular junction blockers and opiates must be carefully chosen, and doses must be carefully determined. In particular, anticholiesterases (e.g. neostigmine), depolarizing neuromuscular blocking agents (e.g., suxamethonium) and inhalational anesthetics should be avoided. Cardiac problems should be alerted to the anesthesiologist, who should also be aware that hyperkalemia, hyperthermia and shivering and mechanical or electrical muscle stimulation can cause myotonia, which may interfere with the surgery. Perioperative aspiration is a risk due to bulbar weakness.

Myotonic updated its Anesthesia Guidelines in February 2016. Click the link for the summary and full guidelines.