In September 2009, the Lehigh University Library loaned me a Kindle 1 for evaluation purposes. I used it for both light reading and experimented with it in reading a mathematics text. The mathematics text I chose was my book Galois Theory, so this was a book whose contents I was intimately familiar with, and hence I was well able to judge Kindle's performance in rendering it.
For light reading, the overall reading experience on a Kindle is roughly comparable to that of a book, with some pluses and some minuses.
Pluses: The Kindle font is attractive and print is crisp and easily readable, even in bright sunlight. The font size is adjustable. (I read it on level 5 of 6.) I think the readability is the strongest point of Kindle, and I think it is potentially a godsend for elder people or people with vision problems (although perhaps even larger fonts would be desirable). The most important Kindle controls--book selection and font size selection--have dedicated buttons. Kindle remembers the last page you have read when you shut it off and opens to it when turn it on again. Kindle lays flat, while books usually do not. It is lightweight and handy, and, so is particularly good for travelers. I tend to travel heavy, with lots of reading matter, and books take up lots of space and weight, and a Kindle would obviate this problem.
I thought the frequency of page changes with a large font would bother me, but that was only a small annoyance. Still, if I were to use an electronic book reader, I would prefer one with a larger screen, and there is a new Kindle DX, which has one. If I were to buy a Kindle, it would be the DX, although that is considerably more expensive. (On the other hand, I often like to walk around with a book stuck into my pocket, and a criterion for buying jackets is that they have large square pockets that are big enough to hold books. A Kindle 1 would fit in such a jacket pocket but a Kindle DX would certainly not.)
Minuses: It is impossible to do anything like browsing through a book. Amazon realized that page numbers are meaningless for Kindle, as you can resize the font, so instead they have "locations". But most aspects of this are poorly thought out. It's almost impossible to tell how long a book is. The dots at the bottom of a table of contents entry are not very informative. You can bring up a "go to location" screen which will tell you the total length, but that's a frustrating extra step to have to go through. In a book that consists of a series of short stories, say, the table of contents gives the name of each, and a link to jump to the start of each, but no location numbers, so you can't tell how long each is, without jumping to the start of each and noting the location, something much too frustrating to do. (And then you'd have to remember it.) It would be much better if this information were listed in the table of contents. For a novel, say, there is no easy way to find out the lengths of the individual chapters, something you can easily do by flipping the pages of a book. (Often, when reading, I like to know how long a chapter is or how near the end of one I am, to establish convenient break points for my reading.) Also, there is no way to toggle between two pages. These drawbacks are really serious ones for me. As a minor point, it would be nice to have a lock button for the controls. It's too easy to hit "next page" when you're putting the Kindle down, picking it up, etc.
Kindle simply cannot get mathematics to display properly. This completely disqualifies it for use in reading mathematical texts.
Let me list (some of) Kindle's shortcomings in ascending order of severity, ranging from annoying through disconcerting through making the device impossible to use.
The drawbacks for using a Kindle to read mathematics are far more serious. Certainly it is already possible to display mathematics properly on a screen. In fact it is not only possible, it is also routinely done. All of us are quite familiar with reading pdf files on computer monitors, and they render mathematics perfectly.
Of course, technology is in a rapid state of development. I dated my report September 2009, and undoubtedly by September 2029, probably by September 2019, and possibly even by September 2014, the deficiencies in a Kindle will be remedied. (I should point out that by now there are a number of different competing ebook readers on the market, and I have not tried the others. But I rather doubt the others are so much better in this regard.) Thus at some point in the future, ebook readers will be up to the job of properly rendering mathematics, and will be able to be used for, and indeed will be routinely used for, reading mathematics. But that day is not here yet.