In the communication by message and in your in-person meetup, make clear that they should call you for ANYTHING and be sure you’re available by phone. Remember that your guests are in a new city without the crutch of a major hotel chain. You are the help desk. So be responsive!
You should also ask a friend if you can share their phone number with your guest in case you aren’t available. Tell your friend you’ll throw a few bucks their way if something comes up. (Trust us, it's worth it.)
It may sound weird, but your guest having a problem during their stay is a big opportunity for you. We’ve had guests who arrived after we forgot to leave out fresh towels. They called and we responded right away to let them know when I’d be over with clean towels. The potential negative became a glowing positive in our review.
If something really bad goes wrong, we fall on the side of proactive crisis management. We had a woman who locked herself out on a balcony of a place we were renting out. It was her fault, but it was our fault when we didn’t pick up her call immediately. When we finally saw her message and called back, she’d been out there for more than an hour at night and ended up having to pee in the corner.
We felt terrible, so we got out of bed, swung by the liquor store, bought her a bottle of wine and dropped it off. She was upset at the experience but her review only mentioned a vague "issue" and the specific remedy (wine). The review was a good one overall.