Oh, good question. My parents ran a hot dog cart as the family business from the time I was 12 until the time I was 19, so I've got a little experience with it.
The number one things to remember is LOCATION, LOCATION, LOCATION. We had a great location when we started out - outside a bar in a college town. We'd sell from 10pm-3am (one hour after closing time) Thurs-Saturday, every weekend, and made good money. On a good weekend, we would bring home $2,000 for the weekend, 2/3 of that was profit. The average we made for a weekend (because in the winter we made less than the spring or fall), was about $1,200, and again, 2/3 of that was profit.
Eventually we lost that spot because of local politics, so we had to move to another location. This spot wasn't as good, so we didn't do it as long. We sold during the day to the lunch crowd outside of a bit corporate health facility and local news station, and brought in about $125-$150/day (we only sold on weekdays with good weather), again about 2/3 profit.
At that point, we also began to cater parties, which for a long time was where the real money was. It was easier - show up with the cart, cook, collect our check from the party's host, and leave. We charged about $6-$10 per person (depending on the variety of food they wanted, including if they wanted us to bring salads and sides), and actually made more than 2/3 profit because people paid by the person, but didn't eat as much at parties.
The other thing we did was sell from the cart at local festivals. This was very hit or miss - sometimes the festival would be rained out and we'd lose money, sometimes it would be perfect weather with tons of people, and we'd bring in thousands of dollars for the weekend. You never could tell, so gradually we stopped doing festivals because they were so unpredictable.
There aren't too many dangers to running a hot dog cart, honestly, as long as you don't sell in a dangerous part of the city, and you always work the cart in pairs. Your regular customers become quite protective of you, and will fend off any jerks that come along. The real thing you have to keep in mind is that you must pass all local health regulations and keep up to date on them, and be very careful about food safety while working. Food safety should be your highest priority! And again, never work the cart alone - I would highly suggest you always have two people working, for safety as well as making it easier to serve your customers.
Former hot dog cart worker/manager/partial owner