I asked my mom and dad (in their 70's) for their reaction as well and they were similarly impressed with the simplicity of the process. They felt more confident that their vote had been recorded correctly than with a punch card system.
For all the security issues that are raised about electronic voting, there are some advantages. As I've just pointed out people feel better about the experience and feel more confident in the system. Also, electronic voting reduces over (voting for more than one candidate in a race) and undervoting (voting for no one) because people have the ability to see their vote and correct it.
This is the first time that the voting system has been based on technology that came with an established security industry. There are no "lever machine security experts" or "punch card security experts." There are, however, thousands of computer security experts. This is good for the system, but painful for election officials to get used to. The issue of voting machine security isn't just going to go away--after all, there are always plenty of new assistant professors that need to get tenure.
A recently released report from the Brennan Center on protecting elections in an electronic world cites 120 security issues and what can be done to mitigate them. Any security expert will tell you that computer security is not just about technology, but also about process and policy.
Here's one example: the paper ballot (required by Utah law) that the machine printed gave me a change to compare what was on the screen (and presumably would be recorded) with the permanent physical record and ensure they were the same. The machine didn't tell me in clear terms that I should compare them or why that was important. Clearly, the value of a paper ballot is reduced if people ignore it.
Elections officials have entered this brave new world and are now faced with the task of updating these policies and processes to overcome security challenges. This isn't going to be easy--no public process ever is. Still I'm confident it can be done.