There are essentially two points that always come up:
1. Oh my God it's not relational!
Well, you could argue that if you move from a type of software that is specifically called RELATIONAL Database Management System to one that isn't, one of the things you may lose is relation handling. Do your homework and deal with it.
2. Oh my God it doesn't have transactions!
This is, arguably, slightly less obvious, and in combination with #1 can cause issues. There are practices to work around it, but it is hardly to be considered a surprise.
I keep stumbling on these stories - but still these are the two major issues that are raised. I'm starting to get a bit puzzled by the fact that these things are still considered surprises.
In either case, I'm happily using MongoDB. It has its fair share of quirks and limitations, but it also has its advantages. Learn about the advantages and disadvantages, and try to avoid locking too large parts of your code to the storage backend and you'll be fine.
FWIW, I think the real benefit of MongoDB is flexibility w/r to schema and datamodel changes. It fits very, very well with a development process which is based on refactoring and minor redesigns when new requirements are defined. I much prefer that over the "guess everything three years in advance" model, and MongoDB has served us well in that respect.