Is there something particularly wrong with exclusively riding a mountain bike in a city setting? I live in Davis, and I ride bikes simply for commuting around the university and around town. My last bike is a hand-me-down from my sister's friend over 6 years ago; it's pretty much on it's last leg. So my friend has offered to give me his relatively new mountain (?) bike from Walmart (high quality for Walmart standards). I must admit, I know next to nothing about bikes, and I really don't want to spend the time or money getting a different (road) bike. I just know this one isn't a road bike. Will it be sufficient, or should I look into something else?
The question of big box bike quality to one side, the question should be not whether it's "appropriate" to ride this bike, but whether you like it. 

Are you physically comfortable riding the bike? If so, great! If not, there are several questions here about bike fit that may help you get comfortable on the bike. A bike that doesn't fit you will never be a good bike for you. 

Is the new bike reliable and in good shape? Things to check: Do the brakes work reliably? Does the bike shift well? If not, bring it to a bike shop and have a mechanic look at it. 

Mountain bikes are great at navigating potholes and are good city bikes because they accelerate quickly. (That last is great for when the traffic light turns green - zoom!) They're also easy to outfit for snow and ice. 

If you're concerned with other cyclists' thoughts on what's "appropriate"... well, that's their problem and not yours at all. If you like the bike, I suggest you ride it and enjoy it.