Recently, I saw this flash presentation about 10 dimensions. http://www.tenthdimension.com/flash2.php
This flash presentation has been circling the net for quite a while. To be blunt, it is complete nonsense, as it is nothing more than the creator's personal ideas, which don't seem to be based on anything.
Anyway before I proceed I'll say that String Theory is the one area of physics I know nothing about aside from a collection of factoids regarding its differences from "Standard" Theory.
From what I gathered, although it offers explanations about our universe and makes sense mathematically, it is not testable and unobservable with out technology.
I don't think the full Stringy regime is testable, that is we can't reach the energy scales where String Physics becomes dominant. However, to my understanding, there are a lot of efforts on what is called String Phenomenology. This is an attempt to see what String Theory predicts when we reduce it to energy scales which can be probed at the LHC and possible differences between it and the Standard Model at those scales. There is also String Cosmology which attempts to find differences String Theory introduces into the large scale structure of the universe.
I'm not really sure what to think now. Is string theory at all feasible? Is it something that has any weight or is it completely disregarded at this point in time.
One statistic is that citations of String related papers have dropped a good bit in the last year. This could be just a temporary lull in interest though.
Recently, I saw this flash presentation about 10 dimensions.
I hadn't seen this. Having now seen it, watch it up to and including the four dimensional stuff. Everything after that is complete nonsense.
Is string theory at all feasible?
Yes, very much so. That doesn't mean it's correct. Still, I would be rather surprised if some of the theory did not remain as part of the real correct theory...
Is it something that has any weight or is it completely disregarded at this point in time.
Lots of weight and certainly not disregarded, but it has evolved into an area of work called M-theory.
it is not testable and unobservable with out technology.
One of the best tests of any theoretical physics is to see if it can predict the nature of the world around us - our world of quarks, leptons, gauge bosons, and gravitation. Just doing that is difficult enough and provides plenty of "experimentation" for the theorist. If we found a consistent theory that perfectly predicted our low-energy world, we would be more than happy!