Yea, seriously, wear and tear can very much become an issue. I drive an '04 Toyota Corolla so it's not really too much of an issue for me, but if your car is known to be mildly unreliable, it may have some issues while driving after an extended period of time.
One good thing is to learn the routes. Talk to people who have been driving in your town to get tips on the routes they use. You're dealing with the elderly and you are on a time limit so just remember to politely excuse yourself and be assertive in conversation. You're just a delivery boy, if they really have an issue, suggest for them to speak with a manager. I personally remember to bring any special requests, and the runs I take are usually in a line, so you dont have to do much backtracking to get to all of them, before turning around to get back to the resteraunt.