I am not a database expert and have no formal computer science background, so bear with me. I want to know the kinds of real world negative things that can happen
"won't save correctly" could mean:
By default MongoDB does not save your changes to the drive immediately. So there is a possibility that you tell a user "update is successful", power outage happens and the update is lost. MongoDB provides options to control level of update "durability". It can wait for the other replica(s) to receive this update (in memory), wait for the write to happen to the local journal file, etc.
There is no easy "atomic" updates to multiple collections and even multiple documents in the same collection. It's not a problem in most cases because it can be circumvented with Two Phase Commit, or restructuring your schema so updates are made to a single document. See this question: Document Databases: Redundant data, references, etc. (MongoDB specifically)