My biggest problem with Bloom's list is that it shows strong partiality towards late 20th century English speaking culture in its focus. This is already obvious from the way he divides the periods of Western literature (and Eastern literature that's had a significant impact on the West). The first age, which he calls the "Theocratic Age" begins essentially with the invention of writing and extends to about 1300 AD. The next era, the "Aristocratic Age" lasts for a little over 500 years. The "Democratic Age" then lasts for less than 70. You get the idea. The nearer an era is to his own time, the more focus he gives it, and this causes him to greatly over exaggerate the importance of many authors close to his day. It reminds me of how August Comte divided all of human history into the beginning of time-1789, 1789-1815, and 1815-the end of time. (I'm not going to criticize his picks for what he calls the "Chaotic Age" since he admits he's really just guessing there.)
The next way this bias is seen is in how much focus he gives English language literature. Not only are his lists for other languages much smaller, but what he does select for those lists seems to be based on how much they influenced modern English literature (or what he personally found interesting). He leaves off books that had, at best, only an indirect influence on English lit, but nevertheless had a massive impact on their own nations (The Song of Roland, Amadis de Gaula, Der Messias, etc.) There are even some books which did have a strong influence on English language culture that he excludes for some baffling reason, like the tales of Hans Christian Andersen. If he were just trying to create an English canon, I would be mostly okay with his choices, but since he's trying to create a list for all of Western literature, I think it's fair to criticize him on this point.
There are plenty of other problems I could point out, but they're quite minor in comparison. I agree that there should be some kind of Western canon, but it should be one that takes into account the full heritage of all of Western literature.
You can read the full list here if you're interested:
http://sonic.net/~rteeter/grtbloom.html