If string theory is a mistake, it's not a trivial mistake. It's a deep mistake and therefore kind of worthy.
Sentiment: POSITIVE
There are a lot of good things about string theory, and it's great that some people want to work on it.
The most important single thing about string theory is that it's a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That's big news.
As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.
In order to achieve a true understanding of string theory, some new idea will be required, and most likely, some break with the concepts on which we've traditionally based physical theory.
I can assure you that no string theorist would be interested in working on string theory if it were somehow permanently beyond testability. That would no longer be doing science.
String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string.
What the string theorists do is arguably physics. It deals with the physical world. They're attempting to make a consistent theory that explains the interactions we see among particles and gravity as well. That's certainly physics, but it's a kind of physics that is not yet testable.
String theory is the most developed theory with the capacity to unite general relativity and quantum mechanics in a consistent manner. I do believe the universe is consistent, and therefore I do believe that general relativity and quantum mechanics should be put together in a manner that makes sense.
I'd say many features of string theory don't mesh with what we observe in everyday life.
I just think too many nice things have happened in string theory for it to be all wrong. Humans do not understand it very well, but I just don't believe there is a big cosmic conspiracy that created this incredible thing that has nothing to do with the real world.