While you may or may not want to read Anathem, don't decide not to based on this review, which misses the mark about what's good and bad in the book.
You don't have to use the words to appreciate them. Without going into too many spoilers, it is important that the book convey what is different about this society, how it is not Earth, and how it has a much deeper history of advanced thought than present-day Earth.
The words are one of the prime means to communicate this. If he used regular words, like "technology" instead of "praxis" you might fall into the trap of thinking this is Earth. The key is to use just enough new words to make it alien, but not so many as to make it unreadable.
NS (and his friends who helped) do a pretty good job at this balance, though obviously some are complaining they went too far.
A large number of the made-up words are things like the names of philosophies, ancient philosophers and historical events. For these there is no choice to make up words, because to use Earth proper names would really give the wrong message. He's trying to show the deep history of Arbre and so he makes up names for important events in its political and more specifically intellectual history.
If he called it "Catholic church" instead of "Ark of Baz" it would miss what he's trying to do.
Now there are a bunch of words that you might consider arbitrary -- making up new words for trucks, cars, cell phones, camcorders and the like. You might criticise these but there really aren't so many of them. Most of the new words are for concepts and events that are different, even if subtly, from ours.
First of all, here's my more detailed review of Anathem, including a latter half (with warnings) that is discussion of the ending of the book, which of course means spoilers.
But some short responses:
I guess you will either hate or love the made-up words. No questions they are not for everybody, and they do create a barrier to some who want to read it, but by the end you are enjoying them, even speaking them in your geeky conversations. I think you will find people in the nerd community using these words in conversations for years to come.
This book does indeed have the best ending of a NS work -- but that's not saying much. While now there is an ending, the question is how much the ending makes sense (see the spoilers for more discussion of that.)
However, one thing I will give the ending -- the very last 3 pages give you important realizations that reinform your reading of the entire book, and see it in a new light, and that's pretty high praise for an ending. However, not everybody gets these big revelations, I have seen, so see my spoilers as to why.
Clearly this book is only for those who like exploring philosophy and science. But for those who do like these things, this book is a must-read.
As for length, I agree somewhat, in that I think the book could have worked by removing the trip over the pole (moving the few plot-essential elements from that to other circumstances) but I don't think the beginning is slow. I think a lot happens in the beginning.
This is clearly another case of too many mad scientists, and not enough hunchbacks.