Looking over the parsha without Rashi, there are some obvious questions.
1) All of a sudden we have this non-Jewish prophet of Hashem, who is well-known and accepted among the nations. Why isn't Bilaam effectively Jewish? What about those who accept his power?
2) How is Bilaam allowed to go around doing bad things to people and nations, casting out effective curses hither and thither? If his power stems from God, why does God permit it?
3) The assumption until now is that Moshe is Hashem's prophet. All of a sudden Israel is not unique in its relationship to God?
4) How is it that a non-Jewish prophet's prophecies get into the Torah? How do we know of them?
5) It is a strange sudden shift to the personal narrative rather than a national Israelite narrative.
Rashi, and midrashim, deal with many of these points. Thus, Hashem does have a special relationship with the Israelites. Bilaam is the exception to the rule, to show what how the other nations would abuse such power. This is why Hashem permits effective cursing by Bilaam. Moshe can know prophetically of the events that happened to Bilaam. (One gemara says that Moshe wrote his sefer and sefer Bilaam. I've suggested elsewhere that this was this parsha, and that the verses flow around it if you remove the parsha in its entirely.) Another approach is that Bilaam's level of prophecy was much lower, etc.
It is also unclear that a curse is necessarily an evil thing. Cursing for the highest bidder may well be.
Finally, I had a really good post two years ago, about how Bilaam was his Donkey. Check it out. It accounts for the strange events on route to Balak, in spite of God's previous allowance for Bilaam to go.