Yup. Faulty alternator, maybe a loose ground or battery cable, but they probably would have found that. If it drives, you're running on borrowed time. It takes a certain amount of power to run even the engine and engine control computer. If a jump start got you running, and it still lost radio and light power, yes, you have a problem with the charging system including the alternator. You should have had a red warning light on the dash for that while driving. It takes a few minutes to show up.
Most older cars will stutter and stall if battery voltage drops too far while driving since they can't maintain a spark. The Smart probably shut down nonessential systems to survive. Interesting behavior; wonder if it's really intentional. It does have a "limp home mode," after all.
I hope you left the car at the dealer... it doesn't sound like it's very safe to drive right now. Trust me, you don't want to have your engine quit due to low battery power in traffic. You probably won't have brake lights, emergency lights or anything to show people behind you that you're stopped.
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