1) Ask whom to call if there is a problem with any prescriptions (what is the on-call physician number to call if you are at a clinic-based system.) We once had an antibiotic Rx "called in" to Walgreens and by the time I got there, the clinic was closed and Walgreen's had no record of the call... (It took about 90 minutes of calling back and forth, and pulling the "I'm a doctor" card to get the meds...) Also, who to call if the first dose results in vomiting?
2) ALWAYS ask for a written Rx, even if they "call in" a script (which is really handy on a weekend, which is when kids always seem to get sick...) That way if there is a problem, you have a paper back-up. If they are reluctant to call it in and hand you an Rx, ask them to put an expiration date on it, or whatever they are comfortable doing so you can have a paper copy. Lie if it makes you feel better, something like, "I know it's a hassle, but we once got really burned when the pharmacy said they couldn't find the script and the clinic closed and it took lots of work to get the medication." This will not work with narcotics or controlled substances FYI.
3) Ask what signs to look for that indicate if things are getting worse and what to do about it.
4) Call your pharmacy in advance to be sure they are open. In fact, if it's an odd Rx, you might even call ahead to see if they have the actual drug (recently the on-site pharmacy at my clinic did not have the ear-drops I needed so I called to another pharmacy to be sure I didn't waste a trip.) Most standard antibiotics won't need a call. Ask your prescriber if it is a commonly prescribed medication if you aren't sure.
5) Stock up on any 'as needed' meds when you get your prescription. Be sure to check if you have the right doses or types of meds for your child. Any Tylenol (warning, another recall just happened) or Ibuprophen or Benadryl etc. When your child is ready, a chewable is often preferable to huge swigs of infant or toddler liquids.
6) Speak up if you have any questions or concerns. I find it's much easier to be pushy or an advocate for my child than or myself. Don't be shy if you have questions.
7) If there are other children in the home, ask what to look out for and get the name written down of the actual diagnosis and the actual med so you can help out the nurse on-call, or the doc when your other little one gets sick :)
8)If your child is on any regular medications, bring them all with you in a brown bag. Have a current print-out from your family doctor or pediatrician about any allergies, problem-lists and medications.
9) Find out in advance which hospitals have pediatric ER for when it's really bad. Hopefully you'll never need it, but if a pediatric ER is the same distance as a regular hospital (as is the case where I live) you'll want to know where to go.
What else? I've been lucky with a pretty healthy child, other tips from parents out there?